From 09f7f9432bb8bb5dfe4f47e8d3ba00a2fe461f53 Mon Sep 17 00:00:00 2001
From: James Smith <js5@sanger.ac.uk>
Date: Sun, 3 Apr 2022 22:31:58 +0100
Subject: Update README.md

---
 challenge-158/james-smith/README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/challenge-158/james-smith/README.md b/challenge-158/james-smith/README.md
index 342202ccbf..a81bb61a28 100644
--- a/challenge-158/james-smith/README.md
+++ b/challenge-158/james-smith/README.md
@@ -94,7 +94,7 @@ sub additive_primes_split_sum0 {
  * `split`            -  75%
  * `sum0 split`       -  45%
 
-# Challenge 2 - First series buban primes
+# Challenge 2 - First series cuban primes
 
 ***Write a script to compute first series cuban primes <= 1000. (First series cuban primes have the form `((x+1)^3-x^3)/(x+1-x)` = `3x^2+3x+1`)***
 
-- 
cgit 


From 9bd3a76992e2c016e85625c4d94969ec05ca7a43 Mon Sep 17 00:00:00 2001
From: drbaggy <js5@sanger.ac.uk>
Date: Mon, 4 Apr 2022 07:32:24 +0100
Subject: 159

---
 challenge-159/james-smith/README.md    | 130 +++++++++------------------------
 challenge-159/james-smith/blog.txt     |   1 +
 challenge-159/james-smith/perl/ch-1.pl |  20 +++++
 challenge-159/james-smith/perl/ch-2.pl |  39 ++++++++++
 4 files changed, 94 insertions(+), 96 deletions(-)
 create mode 100644 challenge-159/james-smith/blog.txt
 create mode 100644 challenge-159/james-smith/perl/ch-1.pl
 create mode 100644 challenge-159/james-smith/perl/ch-2.pl

diff --git a/challenge-159/james-smith/README.md b/challenge-159/james-smith/README.md
index 342202ccbf..cb08f40942 100644
--- a/challenge-159/james-smith/README.md
+++ b/challenge-159/james-smith/README.md
@@ -1,6 +1,6 @@
-[< Previous 157](https://github.com/drbaggy/perlweeklychallenge-club/tree/master/challenge-157/james-smith) |
-[Next 159 >](https://github.com/drbaggy/perlweeklychallenge-club/tree/master/challenge-159/james-smith)
-# The Weekly Challenge 158
+[< Previous 156](https://github.com/drbaggy/perlweeklychallenge-club/tree/master/challenge-156/james-smith) |
+[Next 160 >](https://github.com/drbaggy/perlweeklychallenge-club/tree/master/challenge-160/james-smith)
+# The Weekly Challenge 159
 
 You can find more information about this weeks, and previous weeks challenges at:
 
@@ -12,120 +12,58 @@ submit solutions in whichever language you feel comfortable with.
 
 You can find the solutions here on github at:
 
-https://github.com/drbaggy/perlweeklychallenge-club/tree/master/challenge-158/james-smith
+https://github.com/drbaggy/perlweeklychallenge-club/tree/master/challenge-159/james-smith
 
-# Challenge 1 - Additive primes
+# Challenge 1 - Farey Sequence
 
-***Additive primes are prime numbers for which the sum of their decimal digits are also primes.***
+*** You are given a positive number, `$n`. Write a script to compute Farey Sequence of the order `$n`. All rational numbers less than with with denominators less than `$n`
 
 ## The solution
 
-We loop through each prime p, work out the digit sum (by repeated modulo 10/divide by 10) and check that it is prime.
-We craft this as two loops - an outer `for` loop and an inner `do {} while`.
-
-```perl
-use Math::Prime::Util qw(next_prime is_prime);
-
-sub additive_primes {
-  my @res;
-  for(
-    my $p = 2                                             ;
-    my $s = 0,                        ( my $q = $p ) <= $N;
-    (is_prime $s) && (push @res, $p), $p = next_prime $p
-  ) {
-    do { $s += $q % 10 } while $q = int $q / 10;
-  }
-  @res;
-}
-```
-## Output
-```
-2, 3, 5, 7, 11, 23, 29, 41, 43, 47, 61, 67, 83, 89
-```
-## Notes
- * We use a C-style `for` loop, with it's three parts *initialization*, *condition* and *increment*.
- * The *condition* and *increment* statements are complicated, each with two parts separated by `,`s.
- * The *condition* block is called at the start of each loop, and so we use it to initialise the variables as the loop, as well as checking the condition.
- * The *increment* block is called at the end of the loop and so stores the value of `$p` if it is an additive prime, then it increments the loop with the next prime.
- * Rather than doing a split and sum we use repeated dividing and summing, as it is more efficient around 20-30% more efficient. The increased performance is probably due to avoiding the "duality" of perl variables storing numbers as numbers/strings.
-
-## Extra code
-
-Rewritten with single line `for` ... (the original version of the code)
-
-```perl
-sub additive_primes_div {
-  my @res;
-  for(my$p=2; my$s=0,(my $q=$p)<=$N;(is_prime$s)&&(push@res,$p),$p=next_prime$p) {
-    do { $s += $q % 10 } while $q = int $q / 10;
-  }
-  @res;
-}
-```
-
-Alternative form with `for split`:
-
 ```perl
-sub additive_primes_split {
-  my @res;
-  for( my $p = 2; my $s = 0, $p <= $N ; $p = next_prime $p ) {
-    $s+=$_ for split //, $p;
-    push @res, $p if is_prime $s;
+sub farley {
+  my($n,%v) = shift;
+  for my $d (1..$n) {
+    $v{$_/$d}||="$_/$d" for 1..$d;
   }
-  @res;
+  map{$v{$_}}sort{$a<=>$b}keys%v;
 }
 ```
 
-And an alternate using `sum0`...
-
-```perl
-sub additive_primes_split_sum0 {
-  my @res;
-  for( my $p = 2; $p <= $N ; $p = next_prime $p ) {
-    push @res, $p if is_prime sum0 split //, $p;
-  }
-  @res;
-}
-```
+# Challenge 2 - Moebius Number
 
-### Relative performance
+***You are given a positive number `$n`. Write a script to generate the Moebius Number for the given number (see defn below)
 
- * `div`/`mod` method - 100%
- * `split`            -  75%
- * `sum0 split`       -  45%
+## Definition
 
-# Challenge 2 - First series buban primes
+The value of the Moebius number is:
 
-***Write a script to compute first series cuban primes <= 1000. (First series cuban primes have the form `((x+1)^3-x^3)/(x+1-x)` = `3x^2+3x+1`)***
+ * `0` if `$n` has a prime factor
+ * `1` if the number has an even number of prime factors
+ * `-1` otherwise
 
 ## The solution
 
-The solution is rather short. We try each of the value of the sequence `3*$x**2+3*$x+1` in turn up to the value of 1000 (`$N`).
-We output each value which in turn is prime.
-
 ```perl
-(is_prime $_) && say while $N >= ($_ = 3*$x*++$x+1);
-```
-## Output
-```
-7, 19, 37, 61, 127, 271, 331, 397, 547, 631, 919
+sub moebius {
+  my ($n,$p,$r) = (shift,1,1);
+  return -1 if is_prime($n);
+  $n%($p**2) ? ($n%$p && ($r=-$r)) : return 0 while ($p = next_prime $p) < $n;
+  $r;
+}
 ```
-## Notes
- * As we use `$_` as our temporary variable we can use `say` by itself to output it.
- * We use our common trick of `(condition) && (command)` to work as an `command if(condition)` which can be embedded in a postfix loop.
- * There is a "trick" as we increment `$x` half way through the calculation of `$_`.
-   * `$_ = 3*$x**2 + 3*$x + 1` => `$_ = 3 * $x * ($x+1) + 1` => `$_ = 3 * $x * ++$x + 1`
-   * We can replace the `$x+1` by the pre increment operator `++$x` so this becomes `3 * $x * ++$x + 1`.
 
-## Aside
+Expanding this out gives the more readable (but longer)...
 
-Second series cuban primes have the form `((x+2)^3-x^3)/(x+2-x)` = `3x^2+3.2x+4`. We can tweak the code to give:
-
-```perl
-(is_prime $_) && say while $N >= ($_ = 3 * $x * (2 + $x++) + 4);
 ```
+sub moebius_exp {
+  my ($n,$p,$r) = (shift,1,1);
+  return -1 if is_prime($n);
+  while( ($p = next_prime $p ) < $n ) {
+    return 0 unless $n%($p**2);
+    $r=-$r unless $n%$p;
+  }
+  $r;
+}
 
-which outputs:
-```
-13, 109, 193, 433, 769
 ```
diff --git a/challenge-159/james-smith/blog.txt b/challenge-159/james-smith/blog.txt
new file mode 100644
index 0000000000..e631de6584
--- /dev/null
+++ b/challenge-159/james-smith/blog.txt
@@ -0,0 +1 @@
+https://github.com/drbaggy/perlweeklychallenge-club/tree/master/challenge-159/james-smith
diff --git a/challenge-159/james-smith/perl/ch-1.pl b/challenge-159/james-smith/perl/ch-1.pl
new file mode 100644
index 0000000000..5f6402ec41
--- /dev/null
+++ b/challenge-159/james-smith/perl/ch-1.pl
@@ -0,0 +1,20 @@
+#!/usr/local/bin/perl
+
+use strict;
+
+use warnings;
+use feature qw(say);
+use Test::More;
+use Benchmark qw(cmpthese timethis);
+use Data::Dumper qw(Dumper);
+
+say join ', ', farley( $_ ) for 1..10;
+
+sub farley {
+  my($n,%v) = shift;
+  for my $d (1..$n) {
+    $v{$_/$d}||="$_/$d" for 1..$d;
+  }
+  map{$v{$_}}sort{$a<=>$b}keys%v;
+}
+
diff --git a/challenge-159/james-smith/perl/ch-2.pl b/challenge-159/james-smith/perl/ch-2.pl
new file mode 100644
index 0000000000..5c86128a4d
--- /dev/null
+++ b/challenge-159/james-smith/perl/ch-2.pl
@@ -0,0 +1,39 @@
+#!/usr/local/bin/perl
+
+use strict;
+
+use warnings;
+use feature qw(say);
+use Test::More;
+use Benchmark qw(cmpthese timethis);
+use Data::Dumper qw(Dumper);
+use Math::Prime::Util qw(next_prime is_prime);
+
+my @TESTS = (
+  [  5, -1 ],
+  [ 10,  1 ],
+  [ 20,  0 ],
+);
+
+is( moebius(    $_->[0]), $_->[1] ) foreach @TESTS;
+is( moebius_exp($_->[0]), $_->[1] ) foreach @TESTS;
+
+done_testing();
+
+sub moebius {
+  my ($n,$p,$r) = (shift,1,1);
+  return -1 if is_prime($n);
+  $n%($p**2) ? ($n%$p && ($r=-$r)) : return 0 while ($p = next_prime $p) < $n;
+  $r;
+}
+
+sub moebius_exp {
+  my ($n,$p,$r) = (shift,1,1);
+  return -1 if is_prime($n);
+  while( ($p = next_prime $p ) < $n ) {
+    return 0 unless $n%($p**2);
+    $r=-$r unless $n%$p;
+  }
+  $r;
+}
+
-- 
cgit 


From c748d446c61a5f4c1923e88b09bebb75c26997c2 Mon Sep 17 00:00:00 2001
From: Mark <53903062+andemark@users.noreply.github.com>
Date: Mon, 4 Apr 2022 06:34:44 +0000
Subject: Challenge 159 Solutions (Raku)

---
 challenge-159/mark-anderson/raku/ch-1.raku | 24 ++++++++++++++++++++++++
 challenge-159/mark-anderson/raku/ch-2.raku | 14 ++++++++++++++
 2 files changed, 38 insertions(+)
 create mode 100644 challenge-159/mark-anderson/raku/ch-1.raku
 create mode 100644 challenge-159/mark-anderson/raku/ch-2.raku

diff --git a/challenge-159/mark-anderson/raku/ch-1.raku b/challenge-159/mark-anderson/raku/ch-1.raku
new file mode 100644
index 0000000000..652d28a6af
--- /dev/null
+++ b/challenge-159/mark-anderson/raku/ch-1.raku
@@ -0,0 +1,24 @@
+#!/usr/bin/env raku
+
+use Test;
+
+is-deeply farey-seq(5), (0/1, 1/5, 1/4, 1/3, 2/5, 1/2, 3/5, 2/3, 3/4, 4/5, 1/1),                                         'example 1';
+
+is-deeply farey-seq(7), (0/1, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 2/5, 3/7, 1/2, 4/7, 3/5, 2/3, 5/7, 3/4, 4/5, 5/6, 6/7, 1/1), 'example 2';
+
+is-deeply farey-seq(4), (0/1, 1/4, 1/3, 1/2, 2/3, 3/4, 1/1),                                                             'example 3'; 
+
+is farey-seq(100).elems, 3045, 'https://oeis.org/A005728/b005728.txt';
+
+sub farey-seq(\n)
+{
+    return 0/1, 1/n, { next-term($^f, $^s) } ... 1/1;
+    
+    sub next-term(\f, \s)
+    {
+        my (\a, \b) = f.nude;
+        my (\c, \d) = s.nude;
+        my \k = (n + b) div d;
+        (k * c - a) / (k * d - b)
+    }
+}
diff --git a/challenge-159/mark-anderson/raku/ch-2.raku b/challenge-159/mark-anderson/raku/ch-2.raku
new file mode 100644
index 0000000000..5d69eda71d
--- /dev/null
+++ b/challenge-159/mark-anderson/raku/ch-2.raku
@@ -0,0 +1,14 @@
+#!/usr/bin/env raku
+
+use Prime::Factor;
+use Test;
+
+is-deeply ( 1..10)>>.&mobius, ( 1, -1, -1, 0, -1, 1, -1, 0,  0, 1);
+is-deeply (11..20)>>.&mobius, (-1,  0, -1, 1,  1, 0, -1, 0, -1, 0);
+
+sub mobius(\n)
+{
+    my @a = prime-factors(n);
+    return 0 if @a.squish < @a;
+    return @a %% 2 ?? 1 !! -1;
+}
-- 
cgit 


From 14dda6355b6f7ee3734a67fa17f126bfc32e7efd Mon Sep 17 00:00:00 2001
From: Luca Ferrari <fluca1978@gmail.com>
Date: Mon, 4 Apr 2022 09:41:59 +0200
Subject: Task 1 done

---
 challenge-159/luca-ferrari/raku/ch-1.p6 | 16 ++++++++++++++++
 challenge-159/luca-ferrari/raku/ch-2.p6 |  2 ++
 2 files changed, 18 insertions(+)
 create mode 100755 challenge-159/luca-ferrari/raku/ch-1.p6
 create mode 100644 challenge-159/luca-ferrari/raku/ch-2.p6

diff --git a/challenge-159/luca-ferrari/raku/ch-1.p6 b/challenge-159/luca-ferrari/raku/ch-1.p6
new file mode 100755
index 0000000000..e8a45c1b94
--- /dev/null
+++ b/challenge-159/luca-ferrari/raku/ch-1.p6
@@ -0,0 +1,16 @@
+#!raku
+# Perl Weekly Challenge 159
+
+
+sub MAIN( Int $n where { $n > 0 } ) {
+    my $start = 0/1.Rat;
+    my $end   = 1/1.Rat;
+
+    my @farey = $start, $end;
+
+    for 2 ..  $n -> $denominator {
+        @farey.push( |( 1 .. $denominator ).map: * / $denominator );
+    }
+
+    @farey.unique.sort.map(  *.nude.join( '/' ) ).say;
+}
diff --git a/challenge-159/luca-ferrari/raku/ch-2.p6 b/challenge-159/luca-ferrari/raku/ch-2.p6
new file mode 100644
index 0000000000..4f7c3ef22b
--- /dev/null
+++ b/challenge-159/luca-ferrari/raku/ch-2.p6
@@ -0,0 +1,2 @@
+#!raku
+# Perl Weekly Challenge 159
-- 
cgit 


From b736fb2f6a230c678badabac696aa77ac0d6c3e1 Mon Sep 17 00:00:00 2001
From: Luca Ferrari <fluca1978@gmail.com>
Date: Mon, 4 Apr 2022 10:05:53 +0200
Subject: Task 2 done

---
 challenge-159/luca-ferrari/raku/ch-2.p6 | 28 ++++++++++++++++++++++++++++
 1 file changed, 28 insertions(+)
 mode change 100644 => 100755 challenge-159/luca-ferrari/raku/ch-2.p6

diff --git a/challenge-159/luca-ferrari/raku/ch-2.p6 b/challenge-159/luca-ferrari/raku/ch-2.p6
old mode 100644
new mode 100755
index 4f7c3ef22b..5f9a75537e
--- a/challenge-159/luca-ferrari/raku/ch-2.p6
+++ b/challenge-159/luca-ferrari/raku/ch-2.p6
@@ -1,2 +1,30 @@
 #!raku
 # Perl Weekly Challenge 159
+
+sub prime-factors( Int $n ) {
+    my $number = $n;
+    my @factors;
+
+    my $factor = 2;
+    while ( $number > 1 && $factor <= $number ) {
+        if ( $number %% $factor ) {
+            @factors.push: $factor;
+            $number /= $factor;
+        }
+        else {
+            $factor++;
+        }
+    }
+
+    return @factors;
+}
+
+
+sub MAIN( Int $n where { $n > 0 } ) {
+
+    my @prime-factors = prime-factors( $n );
+    '0'.say and exit if @prime-factors.elems != @prime-factors.unique.elems;
+    '1'.say and exit if @prime-factors.unique.elems %% 2;
+    '-1'.say and exit;
+
+}
-- 
cgit 


From b91c8355370302f29a2380e43685737ff644b9f2 Mon Sep 17 00:00:00 2001
From: Luca Ferrari <fluca1978@gmail.com>
Date: Mon, 4 Apr 2022 10:21:30 +0200
Subject: Task 1 done in Pl/Perl

---
 challenge-159/luca-ferrari/postgresql/ch-1.plperl | 39 +++++++++++++++++++++++
 challenge-159/luca-ferrari/postgresql/ch-1.sql    |  1 +
 challenge-159/luca-ferrari/postgresql/ch-2.sql    |  1 +
 3 files changed, 41 insertions(+)
 create mode 100644 challenge-159/luca-ferrari/postgresql/ch-1.plperl
 create mode 100644 challenge-159/luca-ferrari/postgresql/ch-1.sql
 create mode 100644 challenge-159/luca-ferrari/postgresql/ch-2.sql

diff --git a/challenge-159/luca-ferrari/postgresql/ch-1.plperl b/challenge-159/luca-ferrari/postgresql/ch-1.plperl
new file mode 100644
index 0000000000..f14fe72613
--- /dev/null
+++ b/challenge-159/luca-ferrari/postgresql/ch-1.plperl
@@ -0,0 +1,39 @@
+CREATE SCHEMA IF NOT EXISTS pwc159;
+
+CREATE OR REPLACE FUNCTION
+pwc159.farey( int )
+RETURNS SETOF text
+AS $CODE$
+   my ($n) = @_;
+
+   my %farey;
+
+   for my $denominator ( 2 .. $n ) {
+       for my $number ( 1 .. $denominator ) {
+
+           # reduce things like 2/4 to 1/2
+          ( $denominator, $number ) /= $number       if ( $denominator % $number == 0 );
+          ( $denominator, $number ) /= $denominator  if ( $number % $denominator == 0 );
+           
+           $farey{ $number/$denominator } = "$number/$denominator";
+       }
+   }
+
+   # bootstrap
+   return_next( '0/1' );
+
+   my %unique_counter;
+   for my $key ( sort keys( %farey ) ) {
+       # ensure only one item is printed out
+       $unique_counter{ $key }++;
+       next if $unique_counter{ $key } > 1;
+       next if $key == 1;  # last term in the sequence
+       
+       return_next( $farey{ $key } );
+   }
+
+   # end term
+   return_next( '1/1' );
+   return undef;
+$CODE$
+LANGUAGE plperl;
diff --git a/challenge-159/luca-ferrari/postgresql/ch-1.sql b/challenge-159/luca-ferrari/postgresql/ch-1.sql
new file mode 100644
index 0000000000..da8824c0c2
--- /dev/null
+++ b/challenge-159/luca-ferrari/postgresql/ch-1.sql
@@ -0,0 +1 @@
+-- Perl Weekly Challenge 159
diff --git a/challenge-159/luca-ferrari/postgresql/ch-2.sql b/challenge-159/luca-ferrari/postgresql/ch-2.sql
new file mode 100644
index 0000000000..da8824c0c2
--- /dev/null
+++ b/challenge-159/luca-ferrari/postgresql/ch-2.sql
@@ -0,0 +1 @@
+-- Perl Weekly Challenge 159
-- 
cgit 


From 8409efbb8a1f588f4bb1d0e4134cdc03b6c6d7f8 Mon Sep 17 00:00:00 2001
From: Luca Ferrari <fluca1978@gmail.com>
Date: Mon, 4 Apr 2022 10:34:19 +0200
Subject: Task 1 done in plpgsql

---
 challenge-159/luca-ferrari/postgresql/ch-1.sql | 69 ++++++++++++++++++++++++++
 1 file changed, 69 insertions(+)

diff --git a/challenge-159/luca-ferrari/postgresql/ch-1.sql b/challenge-159/luca-ferrari/postgresql/ch-1.sql
index da8824c0c2..1ebd6c5112 100644
--- a/challenge-159/luca-ferrari/postgresql/ch-1.sql
+++ b/challenge-159/luca-ferrari/postgresql/ch-1.sql
@@ -1 +1,70 @@
 -- Perl Weekly Challenge 159
+
+
+CREATE SCHEMA IF NOT EXISTS pwc159;
+
+
+CREATE OR REPLACE FUNCTION
+pwc159.farey_not_unique( n int )
+RETURNS TABLE( f text, v numeric )
+AS $CODE$
+DECLARE
+     numerator   int;
+     denominator int;
+     dd          int;
+     nn          int;
+BEGIN
+
+        -- bootstrap term
+        SELECT '0/1', 0
+        INTO f, v;
+
+        RETURN NEXT;
+
+
+        FOR denominator IN 2 .. n  LOOP
+            FOR numerator IN  1 .. denominator  LOOP
+                nn := numerator;
+                dd := denominator;
+
+                IF dd % nn = 0 THEN
+                   dd := dd / nn;
+                   nn := 1;
+                END IF;
+
+                IF nn % dd = 0 THEN
+                   nn := nn / dd;
+                   dd := 1;
+                END IF;
+
+                IF nn / dd = 1 THEN
+                   CONTINUE;
+                END IF;
+
+                SELECT nn || '/' || dd, nn/dd::numeric
+                INTO  f, v;
+
+                RETURN NEXT;
+
+            END LOOP;
+        END LOOP;
+
+        -- end term
+        SELECT '1/1', 1
+        INTO f, v;
+
+        RETURN NEXT;
+
+RETURN;
+END
+$CODE$
+LANGUAGE plpgsql;
+
+
+WITH farey AS (
+     SELECT distinct( f ), v
+     FROM pwc159.farey_not_unique( 5 )
+     ORDER BY v
+)
+SELECT f
+FROM farey;
-- 
cgit 


From fba5916d12a035d52cc82ced5536c6bcf531a22f Mon Sep 17 00:00:00 2001
From: Scimon <simon.proctor@gmail.com>
Date: Mon, 4 Apr 2022 09:47:39 +0100
Subject: Challenge 1

---
 challenge-159/simon-proctor/raku/ch-1.raku | 6 ++++++
 1 file changed, 6 insertions(+)
 create mode 100644 challenge-159/simon-proctor/raku/ch-1.raku

diff --git a/challenge-159/simon-proctor/raku/ch-1.raku b/challenge-159/simon-proctor/raku/ch-1.raku
new file mode 100644
index 0000000000..c94a0e7bb4
--- /dev/null
+++ b/challenge-159/simon-proctor/raku/ch-1.raku
@@ -0,0 +1,6 @@
+#!/usr/bin/env raku
+
+# Output the Farey Sequence of order n
+sub MAIN ( Int \n ) {
+    ((0..n) X/ (1..n)).grep( * <= 1 ).unique.sort.map( *.nude ).map( { "@_[0]/@_[1]" } ).join(", ").say
+}
-- 
cgit 


From 13809215bbd6899853b500386805feffe995bbe4 Mon Sep 17 00:00:00 2001
From: Roger Bell_West <roger@firedrake.org>
Date: Mon, 4 Apr 2022 09:49:42 +0100
Subject: Solutions for challenge #159

---
 challenge-159/roger-bell-west/javascript/ch-1.js |  97 +++++++++
 challenge-159/roger-bell-west/javascript/ch-2.js |  94 +++++++++
 challenge-159/roger-bell-west/kotlin/ch-1.kt     |  72 +++++++
 challenge-159/roger-bell-west/kotlin/ch-2.kt     |  94 +++++++++
 challenge-159/roger-bell-west/lua/ch-1.lua       | 104 +++++++++
 challenge-159/roger-bell-west/lua/ch-2.lua       |  97 +++++++++
 challenge-159/roger-bell-west/perl/ch-1.pl       |  56 +++++
 challenge-159/roger-bell-west/perl/ch-2.pl       |  78 +++++++
 challenge-159/roger-bell-west/postscript/ch-1.ps | 256 +++++++++++++++++++++++
 challenge-159/roger-bell-west/postscript/ch-2.ps | 217 +++++++++++++++++++
 challenge-159/roger-bell-west/python/ch-1.py     |  50 +++++
 challenge-159/roger-bell-west/python/ch-2.py     |  75 +++++++
 challenge-159/roger-bell-west/raku/ch-1.p6       |  51 +++++
 challenge-159/roger-bell-west/raku/ch-2.p6       |  74 +++++++
 challenge-159/roger-bell-west/ruby/ch-1.rb       |  52 +++++
 challenge-159/roger-bell-west/ruby/ch-2.rb       |  36 ++++
 challenge-159/roger-bell-west/rust/ch-1.rs       |  97 +++++++++
 challenge-159/roger-bell-west/rust/ch-2.rs       |  84 ++++++++
 18 files changed, 1684 insertions(+)
 create mode 100755 challenge-159/roger-bell-west/javascript/ch-1.js
 create mode 100755 challenge-159/roger-bell-west/javascript/ch-2.js
 create mode 100644 challenge-159/roger-bell-west/kotlin/ch-1.kt
 create mode 100644 challenge-159/roger-bell-west/kotlin/ch-2.kt
 create mode 100755 challenge-159/roger-bell-west/lua/ch-1.lua
 create mode 100755 challenge-159/roger-bell-west/lua/ch-2.lua
 create mode 100755 challenge-159/roger-bell-west/perl/ch-1.pl
 create mode 100755 challenge-159/roger-bell-west/perl/ch-2.pl
 create mode 100644 challenge-159/roger-bell-west/postscript/ch-1.ps
 create mode 100644 challenge-159/roger-bell-west/postscript/ch-2.ps
 create mode 100755 challenge-159/roger-bell-west/python/ch-1.py
 create mode 100755 challenge-159/roger-bell-west/python/ch-2.py
 create mode 100755 challenge-159/roger-bell-west/raku/ch-1.p6
 create mode 100755 challenge-159/roger-bell-west/raku/ch-2.p6
 create mode 100755 challenge-159/roger-bell-west/ruby/ch-1.rb
 create mode 100755 challenge-159/roger-bell-west/ruby/ch-2.rb
 create mode 100755 challenge-159/roger-bell-west/rust/ch-1.rs
 create mode 100755 challenge-159/roger-bell-west/rust/ch-2.rs

diff --git a/challenge-159/roger-bell-west/javascript/ch-1.js b/challenge-159/roger-bell-west/javascript/ch-1.js
new file mode 100755
index 0000000000..c18b03883d
--- /dev/null
+++ b/challenge-159/roger-bell-west/javascript/ch-1.js
@@ -0,0 +1,97 @@
+#! /usr/bin/node
+
+function deepEqual(a,b)
+{
+    if( (typeof a == 'object' && a != null) &&
+        (typeof b == 'object' && b != null) )
+    {
+        var count = [0,0]
+        for( var key in a) count[0]++
+        for( var key in b) count[1]++
+        if( count[0]-count[1] != 0) {return false}
+        for( var key in a)
+        {
+            if(!(key in b) || !deepEqual(a[key],b[key])) {return false}
+        }
+        for( var key in b)
+        {
+            if(!(key in a) || !deepEqual(b[key],a[key])) {return false}
+        }
+        return true
+    }
+    else
+    {
+        return a === b
+    }
+}
+
+function gcd (m0,n0) {
+    let m=m0
+    let n=n0
+    while (n != 0) {
+        [m,n]=[n,m % n]
+    }
+    return m
+}
+
+function lcm (m,n) {
+    return m/gcd(m,n)*n
+}
+
+function lcmseries(a0,b) {
+    let a=a0
+    for (let i=a+1;i <= b;i++) {
+        a=lcm(a,i)
+    }
+    return a
+}
+
+function farey (n) {
+    let l=lcmseries(2,n)
+    let d=new Map()
+    let s=[]
+    for (let i=1;i <= n;i++) {
+        let m=l/i
+        for (let j=0;j <= i;j++) {
+            let k=m*j
+            if (!d.has(k)) {
+                d.set(k,[j,i])
+                s.push(k)
+            }
+        }
+    }
+    s.sort(function(a,b) {
+        return a-b;
+    })
+    return s.map(i => d.get(i))
+}
+
+if (deepEqual(farey(5),[
+    [0, 1], [1, 5], [1, 4], [1, 3], [2, 5], [1, 2], [3, 5], [2, 3],
+    [3, 4], [4, 5], [1, 1]
+])) {
+    process.stdout.write("Pass")
+} else {
+    process.stdout.write("FAIL")
+}
+process.stdout.write(" ");
+
+if (deepEqual(farey(7),[
+    [0, 1], [1, 7], [1, 6], [1, 5], [1, 4], [2, 7], [1, 3], [2, 5],
+    [3, 7], [1, 2], [4, 7], [3, 5], [2, 3], [5, 7], [3, 4], [4, 5],
+    [5, 6], [6, 7], [1, 1]
+])) {
+    process.stdout.write("Pass")
+} else {
+    process.stdout.write("FAIL")
+}
+process.stdout.write(" ");
+
+if (deepEqual(farey(4),[
+    [0, 1], [1, 4], [1, 3], [1, 2], [2, 3], [3, 4], [1, 1]
+])) {
+    process.stdout.write("Pass")
+} else {
+    process.stdout.write("FAIL")
+}
+process.stdout.write("\n");
diff --git a/challenge-159/roger-bell-west/javascript/ch-2.js b/challenge-159/roger-bell-west/javascript/ch-2.js
new file mode 100755
index 0000000000..619b239213
--- /dev/null
+++ b/challenge-159/roger-bell-west/javascript/ch-2.js
@@ -0,0 +1,94 @@
+#! /usr/bin/node
+
+function genprimes(mx) {
+    let primesh=new Set([2,3])
+    for (let i = 6; i <= mx; i += 6) {
+        for (let j = i-1; j <= i+1; j += 2) {
+            if (j <= mx) {
+                primesh.add(j);
+            }
+        }
+    }
+    let q=[2,3,5,7];
+    let p=q.shift();
+    let mr=Math.floor(Math.sqrt(mx));
+    while (p <= mr) {
+        if (primesh.has(p)) {
+            let i=p*p
+            for (let i=p*p; i <= mx; i += p) {
+                primesh.delete(i);
+            }
+        }
+        if (q.length < 2) {
+            q.push(q[q.length-1]+4);
+            q.push(q[q.length-1]+2);
+        }
+        p=q.shift();
+    }
+    let primes=[...primesh];
+    primes.sort(function(a,b) {
+        return a-b;
+    });
+    return primes;
+}
+
+function primefactor (n) {
+    let f=new Map()
+    let m=n
+    for (let p of genprimes(Math.floor(Math.sqrt(n)))) {
+        while (m % p == 0) {
+            m=Math.floor(m/p)
+            if (f.has(p)) {
+                f.set(p,f.get(p)+1)
+            } else {
+                f.set(p,1)
+            }
+            if (m == 1) {
+                break
+            }
+        }
+    }
+    if (m > 1) {
+        if (f.has(m)) {
+            f.set(m,f.get(m)+1)
+        } else {
+            f.set(m,1)
+        }
+    }
+    return f
+}
+
+function moebius (n) {
+    let z=0
+    for (let v of primefactor(n).values()) {
+        if (v > 1) {
+            return 0
+        }
+        z++
+    }
+    if (z % 2 == 0) {
+        return 1
+    }
+    return -1
+}
+
+if (moebius(5) == -1) {
+    process.stdout.write("Pass");
+} else {
+    process.stdout.write("FAIL");
+}
+process.stdout.write(" ");
+
+if (moebius(10) == 1) {
+    process.stdout.write("Pass");
+} else {
+    process.stdout.write("FAIL");
+}
+process.stdout.write(" ");
+
+if (moebius(20) == 0) {
+    process.stdout.write("Pass");
+} else {
+    process.stdout.write("FAIL");
+}
+process.stdout.write("\n");
diff --git a/challenge-159/roger-bell-west/kotlin/ch-1.kt b/challenge-159/roger-bell-west/kotlin/ch-1.kt
new file mode 100644
index 0000000000..362aa1c7f6
--- /dev/null
+++ b/challenge-159/roger-bell-west/kotlin/ch-1.kt
@@ -0,0 +1,72 @@
+import kotlin.math.*
+
+fun gcd(m0: Int,n0: Int): Int {
+    var m=m0
+    var n=n0
+    while (n != 0) {
+        val tmp=m % n
+        m = n
+        n = tmp
+    }
+    return m
+}
+
+fun lcm(m: Int,n: Int): Int {
+    return m/gcd(m,n)*n
+}
+
+fun lcmseries(s: List<Int>): Int {
+    return s.reduce { acc, x -> lcm(acc,x) }
+}
+
+fun farey(n: Int): List<Pair<Int,Int>> {
+    val l = lcmseries((2..n).toList())
+    var d = mutableMapOf<Int,Pair<Int,Int>>()
+    var s = ArrayList<Int>()
+    for (i in 1..n) {
+        val m = l / i
+        for (j in 0..i) {
+            val k = m * j
+            if (!d.contains(k)) {
+                d[k]=Pair(j,i)
+                s.add(k)
+            }
+        }
+    }
+    s.sort()
+    return s.map {d[it]!!}
+}
+
+fun main() {
+    if (farey(5) == listOf(
+            Pair(0, 1), Pair(1, 5), Pair(1, 4), Pair(1, 3),
+            Pair(2, 5), Pair(1, 2), Pair(3, 5), Pair(2, 3),
+            Pair(3, 4), Pair(4, 5), Pair(1, 1)
+    )) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    print(" ")
+    if (farey(7) == listOf(
+            Pair(0, 1), Pair(1, 7), Pair(1, 6), Pair(1, 5),
+            Pair(1, 4), Pair(2, 7), Pair(1, 3), Pair(2, 5),
+            Pair(3, 7), Pair(1, 2), Pair(4, 7), Pair(3, 5),
+            Pair(2, 3), Pair(5, 7), Pair(3, 4), Pair(4, 5),
+            Pair(5, 6), Pair(6, 7), Pair(1, 1)
+    )) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    print(" ")
+    if (farey(4) == listOf(
+            Pair(0, 1), Pair(1, 4), Pair(1, 3), Pair(1, 2),
+            Pair(2, 3), Pair(3, 4), Pair(1, 1)
+    )) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    println("")
+}
diff --git a/challenge-159/roger-bell-west/kotlin/ch-2.kt b/challenge-159/roger-bell-west/kotlin/ch-2.kt
new file mode 100644
index 0000000000..8cbe15e254
--- /dev/null
+++ b/challenge-159/roger-bell-west/kotlin/ch-2.kt
@@ -0,0 +1,94 @@
+import kotlin.math.*
+
+fun genprimes(mx: Int): ArrayList<Int> {
+    var primesh=mutableSetOf<Int>()
+    for (i in 2..3) {
+        primesh.add(i)
+    }
+    for (i in 6..mx+1 step 6) {
+        for (j in i-1..i+1 step 2) {
+            if (j <= mx) {
+                primesh.add(j)
+            }
+        }
+    }
+    var q=ArrayDeque(listOf(2,3,5,7))
+    var p=q.removeFirst()
+    val mr=sqrt(mx.toDouble()).toInt()
+    while (p <= mr) {
+        if (primesh.contains(p)) {
+            for (i in p*p..mx step p) {
+                primesh.remove(i)
+            }
+        }
+        if (q.size < 2) {
+            q.add(q.last()+4)
+            q.add(q.last()+2)
+        }
+        p=q.removeFirst()
+    }
+    var primes=ArrayList(primesh.distinct())
+    primes.sort()
+    return primes
+}
+
+fun primefactor(n: Int): Map<Int,Int> {
+    var f=mutableMapOf<Int,Int>()
+    var m=n
+    for (p in genprimes(sqrt(m.toDouble()).toInt())) {
+        while (m % p == 0) {
+            m /= p
+            if (f.containsKey(p)) {
+                f[p] = f[p]!!+1
+            } else {
+                f[p]=1
+            }
+        }
+        if (m == 1) {
+            break
+        }
+    }
+    if (m > 1) {
+        if (f.containsKey(m)) {
+            f[m] = f[m]!!+1
+        } else {
+            f[m]=1
+        }
+    }
+    return f
+}
+
+fun moebius(n: Int): Int {
+    var z: Int=0
+    for (v in primefactor(n).values) {
+        if (v > 1) {
+            return 0
+        }
+        z += 1
+    }
+    if (z % 2 == 0) {
+        return 1
+    }
+    return -1
+}
+
+fun main() {
+    if (moebius(5) == -1) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    print(" ")
+    if (moebius(10) == 1) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    print(" ")
+    if (moebius(20) == 0) {
+        print("Pass")
+    } else {
+        print("FAIL")
+    }
+    println("")
+}
diff --git a/challenge-159/roger-bell-west/lua/ch-1.lua b/challenge-159/roger-bell-west/lua/ch-1.lua
new file mode 100755
index 0000000000..d10299f584
--- /dev/null
+++ b/challenge-159/roger-bell-west/lua/ch-1.lua
@@ -0,0 +1,104 @@
+#! /usr/bin/lua
+
+-- by Michael Anderson at
+-- https://stackoverflow.com/questions/8722620/comparing-two-index-tables-by-index-value-in-lua
+function recursive_compare(t1,t2)
+  -- Use usual comparison first.
+  if t1==t2 then return true end
+  -- We only support non-default behavior for tables
+  if (type(t1)~="table") then return false end
+  -- They better have the same metatables
+  local mt1 = getmetatable(t1)
+  local mt2 = getmetatable(t2)
+  if( not recursive_compare(mt1,mt2) ) then return false end
+
+  -- Check each key-value pair
+  -- We have to do this both ways in case we miss some.
+  -- TODO: Could probably be smarter and not check those we've 
+  -- already checked though!
+  for k1,v1 in pairs(t1) do
+    local v2 = t2[k1]
+    if( not recursive_compare(v1,v2) ) then return false end
+  end
+  for k2,v2 in pairs(t2) do
+    local v1 = t1[k2]
+    if( not recursive_compare(v1,v2) ) then return false end
+  end
+
+  return true  
+end
+
+function gcd(m0,n0)
+   local m,n = m0,n0
+   while n ~= 0 do
+      m,n = n,m % n
+   end
+   return m
+end
+
+function lcm(m,n)
+   return m/gcd(m,n)*n
+end
+
+function lcmseries(a,b)
+   local t=1
+   for v = a,b do
+      t = lcm(t,v)
+   end
+   return t
+end
+
+function farey(n)
+   local l=lcmseries(2,n)
+   local d={}
+   local s={}
+   for i = 1,n do
+      local m = l / i
+      for j = 0,i do
+         local k = m * j
+         if d[k] == nil then
+            d[k] = {j,i}
+            table.insert(s,k)
+         end
+      end
+   end
+   table.sort(s)
+   local out={}
+   for k,v in ipairs(s) do
+      table.insert(out,d[v])
+   end
+   return out
+end
+
+if recursive_compare(farey(5),{
+                        {0, 1}, {1, 5}, {1, 4}, {1, 3}, {2, 5},
+                        {1, 2}, {3, 5}, {2, 3}, {3, 4}, {4, 5},
+                        {1, 1}
+                    }) then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+io.write(" ")
+
+if recursive_compare(farey(7),{
+                        {0, 1}, {1, 7}, {1, 6}, {1, 5}, {1, 4},
+                        {2, 7}, {1, 3}, {2, 5}, {3, 7}, {1, 2},
+                        {4, 7}, {3, 5}, {2, 3}, {5, 7}, {3, 4},
+                        {4, 5}, {5, 6}, {6, 7}, {1, 1}
+                    }) then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+io.write(" ")
+
+if recursive_compare(farey(4),{
+                        {0, 1}, {1, 4}, {1, 3}, {1, 2}, {2, 3},
+                        {3, 4}, {1, 1}
+                    }) then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+print("")
diff --git a/challenge-159/roger-bell-west/lua/ch-2.lua b/challenge-159/roger-bell-west/lua/ch-2.lua
new file mode 100755
index 0000000000..1e79067d53
--- /dev/null
+++ b/challenge-159/roger-bell-west/lua/ch-2.lua
@@ -0,0 +1,97 @@
+#! /usr/bin/lua
+
+function genprimes(mx)
+   local primesh = {}
+   for i = 2, 3 do
+      primesh[i] = true
+   end
+   for i = 6, mx, 6 do
+      for j = i-1, i+1, 2 do
+         if j <= mx then
+            primesh[j]=true
+         end
+      end
+   end
+   local q={2,3,5,7}
+   local p=table.remove(q,1)
+   local mr=math.floor(math.sqrt(mx))
+   while p <= mr do
+      if primesh[p] ~= nil then
+         for i = p*p,mx,p do
+            primesh[i] = nil
+         end
+      end
+      if #q < 2 then
+         table.insert(q,q[#q]+4)
+         table.insert(q,q[#q]+2)
+      end
+      p=table.remove(q,1)
+   end
+   local primes = {}
+   for k,v in pairs(primesh) do
+      table.insert(primes,k)
+   end
+   table.sort(primes)
+   return primes
+end
+
+function primefactor(n)
+   local f={}
+   local m=n
+   for k,p in pairs(genprimes(math.floor(math.sqrt(m)))) do
+      while m % p == 0 do
+         m=math.floor(m/p)
+         if f[p] == nil then
+            f[p]=1
+         else
+            f[p] = f[p] + 1
+         end
+         if m==1 then
+            break
+         end
+      end
+   end
+   if m>1 then
+      if f[m] == nil then
+         f[m]=1
+      else
+         f[m] = f[m] + 1
+      end
+   end
+   return f
+end
+
+function moebius(n)
+   local z=0
+   for k,v in pairs(primefactor(n)) do
+      if v > 1 then
+         return 0
+      end
+      z = z + 1
+   end
+   if z % 2 == 0 then
+      return 1
+   end
+   return -1
+end
+
+if moebius(5) == -1 then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+io.write(" ")
+
+if moebius(10) == 1 then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+io.write(" ")
+
+if moebius(20) == 0 then
+   io.write("Pass")
+else
+   io.write("FAIL")
+end
+print("")
diff --git a/challenge-159/roger-bell-west/perl/ch-1.pl b/challenge-159/roger-bell-west/perl/ch-1.pl
new file mode 100755
index 0000000000..e99d1d11f3
--- /dev/null
+++ b/challenge-159/roger-bell-west/perl/ch-1.pl
@@ -0,0 +1,56 @@
+#! /usr/bin/perl
+
+use strict;
+use warnings;
+
+use Test::More tests => 3;
+use List::Util qw(reduce);
+
+is_deeply(farey(5),[
+  [0, 1], [1, 5], [1, 4], [1, 3], [2, 5], [1, 2], [3, 5], [2, 3],
+  [3, 4], [4, 5], [1, 1]
+    ],'example 1');
+
+is_deeply(farey(7),[
+  [0, 1], [1, 7], [1, 6], [1, 5], [1, 4], [2, 7], [1, 3], [2, 5],
+  [3, 7], [1, 2], [4, 7], [3, 5], [2, 3], [5, 7], [3, 4], [4, 5],
+  [5, 6], [6, 7], [1, 1]
+    ],'example 2');
+
+is_deeply(farey(4),[
+  [0, 1], [1, 4], [1, 3], [1, 2], [2, 3], [3, 4], [1, 1]
+    ],'example 3');
+
+sub gcd {
+  my ($m,$n)=@_;
+  while ($n!=0) {
+    ($m,$n)=($n,$m % $n);
+  }
+  return $m;
+}
+
+sub lcm {
+  my ($m,$n)=@_;
+  return $m/gcd($m,$n)*$n;
+}
+
+sub lcmseries {
+  my $s=shift;
+  return reduce {lcm($a,$b)} @{$s};
+}
+
+sub farey {
+  my $n=shift;
+  my $l=lcmseries([2..$n]);
+  my %d;
+  foreach my $i (1..$n) {
+    my $m=$l/$i;
+    foreach my $j (0..$i) {
+      my $k=$m*$j;
+      unless (exists $d{$k}) {
+        $d{$k}=[$j,$i];
+      }
+    }
+  }
+  return [map {$d{$_}} sort {$a <=> $b} keys %d];
+}
diff --git a/challenge-159/roger-bell-west/perl/ch-2.pl b/challenge-159/roger-bell-west/perl/ch-2.pl
new file mode 100755
index 0000000000..4893c02740
--- /dev/null
+++ b/challenge-159/roger-bell-west/perl/ch-2.pl
@@ -0,0 +1,78 @@
+#! /usr/bin/perl
+
+use strict;
+use warnings;
+
+use Test::More tests => 3;
+
+is(moebius(5),-1,'example 1');
+is(moebius(10),1,'example 2');
+is(moebius(20),0,'example 3');
+
+sub genprimes {
+  my $mx=shift;
+  my @primes;
+  {
+    my %primesh=map {$_ => 1} (2,3);
+    for (my $i=6;$i <= $mx+1; $i += 6) {
+      foreach my $j ($i-1,$i+1) {
+        if ($j <= $mx) {
+          $primesh{$j}=1;
+        }
+      }
+    }
+    my @q=(2,3,5,7);
+    my $p=shift @q;
+    my $mr=int(sqrt($mx));
+    while ($p <= $mr) {
+      if ($primesh{$p}) {
+        my $i=$p*$p;
+        while ($i <= $mx) {
+          delete $primesh{$i};
+          $i += $p;
+        }
+      }
+      if (scalar @q < 2) {
+        push @q,$q[-1]+4;
+        push @q,$q[-1]+2;
+      }
+      $p=shift @q;
+    }
+    @primes=sort {$a <=> $b} keys %primesh;
+  }
+  return \@primes;
+}
+
+sub primefactor {
+  my $n=shift;
+  my %f;
+  my $m=$n;
+  foreach my $p (@{genprimes(int(sqrt($n)))}) {
+    while ($m % $p == 0) {
+      $f{$p}++;
+      $m=int($m/$p);
+      if ($m == 1) {
+        last;
+      }
+    }
+  }
+  if ($m > 1) {
+    $f{$m}++;
+  }
+  return \%f;
+}
+
+sub moebius {
+  my $n=shift;
+  my $z=0;
+  foreach my $v (values %{primefactor($n)}) {
+    if ($v>1) {
+      return 0;
+    }
+    $z++;
+  }
+  if ($z % 2 == 0) {
+    return 1;
+  }
+  return -1;
+}
diff --git a/challenge-159/roger-bell-west/postscript/ch-1.ps b/challenge-159/roger-bell-west/postscript/ch-1.ps
new file mode 100644
index 0000000000..30c9d167ab
--- /dev/null
+++ b/challenge-159/roger-bell-west/postscript/ch-1.ps
@@ -0,0 +1,256 @@
+%!PS
+
+% begin library code
+
+/test {
+    /test.count test.count 1 add def
+    {
+        /test.pass test.pass 1 add def
+    } {
+        ( ) print
+        test.count (....) cvs print
+        (-fail) print
+    } ifelse
+} bind def
+
+/test.start {
+    print (:) print
+    /test.pass 0 def
+    /test.count 0 def
+} bind def
+
+/test.end {
+    ( ) print
+    test.count 0 gt {
+        (Passed ) print
+        test.pass (...) cvs print
+        (/) print
+        test.count (...) cvs print
+        ( \() print
+        test.pass 100 mul test.count idiv (...) cvs print
+        (%\)) print
+        (\r\n) print
+    } if
+} bind def
+
+/deepeq {
+    2 dict begin
+    /a exch def
+    /b exch def
+    a type b type eq {
+        a type /dicttype eq {
+            a length b length eq {
+                <<
+                    a {
+                        pop
+                        true
+                    } forall
+                    b {
+                        pop
+                        true
+                    } forall
+                >>
+                true exch
+                {
+                    pop
+                    dup a exch known {
+                        dup b exch known {
+                            dup a exch get exch b exch get deepeq not {
+                                pop false
+                            } if
+                        } {
+                            false
+                        } ifelse
+                    } {
+                        false
+                    } ifelse
+                } forall
+            } {
+                false
+            } ifelse
+        } {
+            a type dup /arraytype eq exch /stringtype eq or {
+                a length b length eq {
+                    true
+                    0 1 a length 1 sub {
+                        dup a exch get exch b exch get deepeq not {
+                            pop false
+                            exit
+                        } if
+                    } for
+                } {
+                    false
+                } ifelse
+            } {
+                a b eq
+            } ifelse
+        } ifelse
+    } {
+        false
+    } ifelse
+    end
+} bind def
+
+/quicksort { % [ a c b ] -> [ a b c ]
+    1 dict begin
+    /arr exch def
+    0 arr length 1 sub quicksort.main
+    arr
+    end
+} bind def
+
+/quicksort.main { % lo hi -> (null)
+    3 dict begin
+    /hi exch def
+    /lo exch def
+    /xit false def
+    lo 0 lt {
+        /xit true def
+    } if
+    hi 0 lt {
+        /xit true def
+    } if
+    lo hi ge {
+        /xit true def
+    } if
+    xit not {
+        /p quicksort.partition def
+        lo p quicksort.main
+        p 1 add hi quicksort.main
+    } if
+    end
+} bind def
+
+/quicksort.partition {
+    3 dict begin
+    /pivot arr hi lo add 2 idiv get def
+    /i lo 1 sub def
+    /j hi 1 add def
+    {
+        {
+            /i i 1 add def
+            arr i get pivot ge {
+                exit
+            } if
+        } loop
+        {
+            /j j 1 sub def
+            arr j get pivot le {
+                exit
+            } if
+        } loop
+        i j ge {
+            j
+            exit
+        } if
+        i j quicksort.swap
+    } loop
+    end
+} bind def
+
+/quicksort.swap {
+    2 dict begin
+    /bi exch def
+    /ai exch def
+    arr ai get
+    arr bi get
+    arr exch ai exch put
+    arr exch bi exch put
+    end
+} bind def
+
+/reduce { % array proc -> value
+    2 dict begin
+    /p exch def
+    /a exch def
+    a 0 get
+    1 1 a length 1 sub {
+        a exch get
+        p
+    } for
+    end
+} bind def
+
+
+/apush { % [a b] c -> [a b c]
+    exch
+    [ exch aload length 2 add -1 roll ]
+} bind def
+
+/map { % array proc -> array
+    2 dict begin
+    /p exch def
+    [ exch
+      {
+          p
+      } forall
+    ]
+} bind def
+
+/keys { % dict -> array of dict keys
+    [ exch
+      {
+          pop
+      } forall
+    ]
+} bind def
+
+% end library code
+
+/gcd {
+    {
+        dup
+        3 1 roll
+        mod
+        dup 0 eq {
+            pop exit
+        } if
+    } loop
+} bind def
+
+/lcm {
+    dup 3 -1 roll
+    dup 4 -1 roll
+    gcd idiv mul
+} bind def
+
+/lcmseries {
+    { lcm } reduce
+} bind def
+
+/farey {
+    7 dict begin
+    /n exch def
+    /l [ 2 1 n { } for ] lcmseries def
+    /d n dup mul dict def
+    1 1 n {
+        /i exch def
+        /m l i idiv def
+        0 1 i {
+            /j exch def
+            /k m j mul def
+            d k known not {
+                d k [ j i ] put
+            } if
+        } for
+    } for
+    d keys quicksort { d exch get } map
+    end
+} bind def
+
+(farey) test.start
+
+5 farey
+[ [0 1] [1 5] [1 4] [1 3] [2 5] [1 2] [3 5] [2 3] [3 4] [4 5] [1 1] ]
+deepeq test
+
+7 farey
+[ [0 1] [1 7] [1 6] [1 5] [1 4] [2 7] [1 3] [2 5] [3 7] [1 2] [4 7]
+  [3 5] [2 3] [5 7] [3 4] [4 5] [5 6] [6 7] [1 1] ]
+deepeq test
+
+4 farey
+[ [0 1] [1 4] [1 3] [1 2] [2 3] [3 4] [1 1] ]
+deepeq test
+
+test.end
diff --git a/challenge-159/roger-bell-west/postscript/ch-2.ps b/challenge-159/roger-bell-west/postscript/ch-2.ps
new file mode 100644
index 0000000000..bfc28ad691
--- /dev/null
+++ b/challenge-159/roger-bell-west/postscript/ch-2.ps
@@ -0,0 +1,217 @@
+%!PS
+
+% begin library code
+
+/test {
+    /test.count test.count 1 add def
+    {
+        /test.pass test.pass 1 add def
+    } {
+        ( ) print
+        test.count (....) cvs print
+        (-fail) print
+    } ifelse
+} bind def
+
+/test.start {
+    print (:) print
+    /test.pass 0 def
+    /test.count 0 def
+} bind def
+
+/test.end {
+    ( ) print
+    test.count 0 gt {
+        (Passed ) print
+        test.pass (...) cvs print
+        (/) print
+        test.count (...) cvs print
+        ( \() print
+        test.pass 100 mul test.count idiv (...) cvs print
+        (%\)) print
+        (\r\n) print
+    } if
+} bind def
+
+/quicksort { % [ a c b ] -> [ a b c ]
+    1 dict begin
+    /arr exch def
+    0 arr length 1 sub quicksort.main
+    arr
+    end
+} bind def
+
+/quicksort.main { % lo hi -> (null)
+    3 dict begin
+    /hi exch def
+    /lo exch def
+    /xit false def
+    lo 0 lt {
+        /xit true def
+    } if
+    hi 0 lt {
+        /xit true def
+    } if
+    lo hi ge {
+        /xit true def
+    } if
+    xit not {
+        /p quicksort.partition def
+        lo p quicksort.main
+        p 1 add hi quicksort.main
+    } if
+    end
+} bind def
+
+/quicksort.partition {
+    3 dict begin
+    /pivot arr hi lo add 2 idiv get def
+    /i lo 1 sub def
+    /j hi 1 add def
+    {
+        {
+            /i i 1 add def
+            arr i get pivot ge {
+                exit
+            } if
+        } loop
+        {
+            /j j 1 sub def
+            arr j get pivot le {
+                exit
+            } if
+        } loop
+        i j ge {
+            j
+            exit
+        } if
+        i j quicksort.swap
+    } loop
+    end
+} bind def
+
+/quicksort.swap {
+    2 dict begin
+    /bi exch def
+    /ai exch def
+    arr ai get
+    arr bi get
+    arr exch ai exch put
+    arr exch bi exch put
+    end
+} bind def
+
+/apush { % [a b] c -> [a b c]
+    exch
+    [ exch aload length 2 add -1 roll ]
+} bind def
+
+/values { % dict -> array of dict values
+    [ exch
+      {
+          exch pop
+      } forall
+    ]
+} bind def
+
+% end library code
+
+/genprimes {
+    /mx exch def
+    /primesh mx dict def
+    2 1 3 {
+        primesh exch true put
+    } for
+    6 6 mx 1 add {
+        dup 1 sub exch 1 add 2 exch {
+            dup mx le {
+                primesh exch true put
+            } {
+                pop
+            } ifelse
+        } for
+    } for
+    /q [ 3 5 7 ] def
+    /qi 0 def
+    /p 2 def
+    /mr mx sqrt cvi def
+    {
+        p mr le not {
+            exit
+        } if
+        primesh p known {
+            p dup mul p mx {
+                primesh exch undef
+            } for
+        } if
+        q length qi sub 2 le {
+            /q q q q length 1 sub get 4 add apush def
+            /q q q q length 1 sub get 2 add apush def
+        } if
+        /p q qi get def
+        /qi qi 1 add def
+    } loop
+    [ primesh { pop } forall ] quicksort
+} bind def
+
+/primefactor {
+    4 dict begin
+    /n exch def
+    /f 1 dict def
+    /m n def
+    n sqrt cvi genprimes {
+        /p exch def
+        {
+            m p mod 0 eq {
+                f p known {
+                    f p f p get 1 add put
+                } {
+                    f p 1 put
+                } ifelse
+                /m m p idiv def
+            } {
+                exit
+            } ifelse
+        } loop
+        m 1 eq {
+            exit
+        }
+    } forall
+    m 1 gt {
+        f m known {
+            f m f m get 1 add put
+        } {
+            f m 1 put
+        } ifelse
+    } if
+    f
+    end
+} bind def
+
+/moebius {
+    1 dict begin
+    /z 0 def
+    primefactor values {
+        1 gt {
+            /z 0 def
+            exit
+        } if
+        /z z 1 add def
+    } forall
+    z 0 eq {
+        0
+    } {
+        z 2 mod 0 eq {
+            1
+        } {
+            -1
+        } ifelse
+    } ifelse
+    end
+} bind def
+
+(moebius) test.start
+5 moebius -1 eq test
+10 moebius 1 eq test
+20 moebius 0 eq test
+test.end
diff --git a/challenge-159/roger-bell-west/python/ch-1.py b/challenge-159/roger-bell-west/python/ch-1.py
new file mode 100755
index 0000000000..d6e05acf97
--- /dev/null
+++ b/challenge-159/roger-bell-west/python/ch-1.py
@@ -0,0 +1,50 @@
+#! /usr/bin/python3
+
+import unittest
+
+from math import gcd
+from functools import reduce
+
+def lcm(m,n):
+  return m//gcd(m,n)*n
+
+def lcmseries(s):
+  return reduce(lcm, s)
+
+def farey(n):
+  l=lcmseries(range(2,n+1))
+  d=dict()
+  s=[]
+  for i in range(1,n+1):
+    m=l // i
+    for j in range(0,i+1):
+      k=m*j
+      if not k in d:
+        d[k]=[j,i]
+        s.append(k)
+  s.sort()
+  return [d[i] for i in s]
+
+class TestFarey(unittest.TestCase):
+
+        def test_ex1(self):
+          self.assertEqual(farey(5),
+                           [[0,1], [1,5], [1,4], [1,3], [2,5], [1,2],
+                            [3,5], [2,3], [3,4], [4,5], [1,1]],
+                           'example 1')
+
+        def test_ex2(self):
+          self.assertEqual(farey(7),
+                           [[0,1], [1,7], [1,6], [1,5], [1,4], [2,7],
+                            [1,3], [2,5], [3,7], [1,2], [4,7], [3,5],
+                            [2,3], [5,7], [3,4], [4,5], [5,6], [6,7],
+                            [1,1]],
+                           'example 2')
+
+        def test_ex3(self):
+          self.assertEqual(farey(4),
+                           [[0,1], [1,4], [1,3], [1,2], [2,3], [3,4],
+                            [1,1]],
+                           'example 3')
+
+unittest.main()
diff --git a/challenge-159/roger-bell-west/python/ch-2.py b/challenge-159/roger-bell-west/python/ch-2.py
new file mode 100755
index 0000000000..125eed5e55
--- /dev/null
+++ b/challenge-159/roger-bell-west/python/ch-2.py
@@ -0,0 +1,75 @@
+#! /usr/bin/python3
+
+import unittest
+
+from math import sqrt,floor,gcd
+from collections import deque
+
+def genprimes(mx):
+  primesh=set(range(2,4))
+  for i in range(6,mx+2,6):
+    for j in range(i-1,i+2,2):
+      if j <= mx:
+        primesh.add(j)
+  q=deque([2,3,5,7])
+  p=q.popleft()
+  mr=floor(sqrt(mx))
+  while p <= mr:
+    if p in primesh:
+      for i in range(p*p,mx+1,p):
+        primesh.discard(i)
+    if len(q) < 2:
+      q.append(q[-1]+4)
+      q.append(q[-1]+2)
+    p=q.popleft()
+  primes=list(primesh)
+  primes.sort()
+  return primes
+
+def primefactor(n):
+  f=dict()
+  m=n
+  for p in genprimes(floor(sqrt(n))):
+    while (m % p == 0):
+      m //= p
+      if p in f:
+        f[p] += 1
+      else:
+        f[p] = 1
+    if m==1:
+      break
+  if m > 1:
+    if m in f:
+      f[m] += 1
+    else:
+      f[m] = 1
+  return f
+
+def moebius(n):
+  z=0
+  for k,v in primefactor(n).items():
+    if v > 1:
+      return 0
+    z += 1
+  if z % 2 == 0:
+    return 1
+  return -1
+
+class TestMoebius(unittest.TestCase):
+
+        def test_ex1(self):
+          self.assertEqual(moebius(5),
+                           -1,
+                           'example 1')
+
+        def test_ex2(self):
+          self.assertEqual(moebius(10),
+                           1,
+                           'example 2')
+
+        def test_ex3(self):
+          self.assertEqual(moebius(20),
+                           0,
+                           'example 3')
+
+unittest.main()
diff --git a/challenge-159/roger-bell-west/raku/ch-1.p6 b/challenge-159/roger-bell-west/raku/ch-1.p6
new file mode 100755
index 0000000000..0c3dee4698
--- /dev/null
+++ b/challenge-159/roger-bell-west/raku/ch-1.p6
@@ -0,0 +1,51 @@
+#! /usr/bin/perl6
+
+use Test;
+
+plan 3;
+
+is-deeply(farey(5),(
+              0 => 1, 1 => 5, 1 => 4, 1 => 3, 2 => 5, 1 => 2, 3 => 5,
+              2 => 3, 3 => 4, 4 => 5, 1 => 1
+          ),'example 1');
+
+is-deeply(farey(7),(
+              0 => 1, 1 => 7, 1 => 6, 1 => 5, 1 => 4, 2 => 7, 1 => 3,
+              2 => 5, 3 => 7, 1 => 2, 4 => 7, 3 => 5, 2 => 3, 5 => 7,
+              3 => 4, 4 => 5, 5 => 6, 6 => 7, 1 => 1
+          ),'example 2');
+
+is-deeply(farey(4),(
+              0 => 1, 1 => 4, 1 => 3, 1 => 2, 2 => 3, 3 => 4, 1 => 1
+          ),'example 3');
+
+sub gcd($m0,$n0) {
+    my ($m,$n)=($m0,$n0);
+    while ($n != 0) {
+        ($m,$n)=($n,$m % $n);
+    }
+    return $m;
+}
+
+sub lcm($m,$n) {
+    return $m/gcd($m,$n)*$n;
+}
+
+sub lcmseries(@s) {
+    return floor(@s.reduce(&lcm));
+}
+
+sub farey($n) {
+    my $l=lcmseries([2..$n]);
+    my %d;
+    for (1..$n) -> $i {
+        my $m = $l div $i;
+        for (0..$i) -> $j {
+            my $k = $m * $j;
+            unless (%d{$k}:exists) {
+                %d{$k}=Pair.new($j,$i);
+            }
+        }
+    }
+    return map {%d{$_}}, sort { $^a <=> $^b }, %d.keys;
+}
diff --git a/challenge-159/roger-bell-west/raku/ch-2.p6 b/challenge-159/roger-bell-west/raku/ch-2.p6
new file mode 100755
index 0000000000..79211760a0
--- /dev/null
+++ b/challenge-159/roger-bell-west/raku/ch-2.p6
@@ -0,0 +1,74 @@
+#! /usr/bin/perl6
+
+use Test;
+
+plan 3;
+
+is(moebius(5),-1,'example 1');
+is(moebius(10),1,'example 2');
+is(moebius(20),0,'example 3');
+
+sub genprimes($mx) {
+    my @primes;
+    {
+        my $primesh=(2,3).SetHash;
+        loop (my $i=6;$i <= $mx+1; $i += 6) {
+            for ($i-1,$i+1) -> $j {
+                if ($j <= $mx) {
+                    $primesh{$j}=True;
+                }
+            }
+        }
+        my $p=2;
+        my @q=[2,3,5,7];
+        my $mr=floor(sqrt($mx));
+        while ($p <= $mr) {
+            if ($primesh{$p}:exists) {
+                my $i=$p*$p;
+                while ($i <= $mx) {
+                    $primesh{$i}:delete;
+                    $i += $p;
+                }
+            }
+            if (@q.elems < 2) {
+                @q.push(@q[*-1]+4);
+                @q.push(@q[*-1]+2);
+            }
+            $p=@q.shift;
+        }
+        @primes=$primesh.keys.sort;
+    }
+    return @primes;
+}
+
+sub primefactor($n) {
+    my %f;
+    my $m=$n;
+    for genprimes(floor(sqrt($n))) -> $p {
+        while ($m % $p == 0) {
+            %f{$p}++;
+            $m=floor($m/$p);
+        }
+        if ($m == 1) {
+            last;
+        }
+    }
+    if ($m > 1) {
+        %f{$m}++;
+    }
+    return %f;
+} 
+
+sub moebius($n) {
+    my $z=0;
+    for primefactor($n).values -> $v {
+        if ($v > 1) {
+            return 0;
+        }
+        $z++;
+    }
+    if ($z % 2 == 0) {
+        return 1;
+    }
+    return -1;
+}
diff --git a/challenge-159/roger-bell-west/ruby/ch-1.rb b/challenge-159/roger-bell-west/ruby/ch-1.rb
new file mode 100755
index 0000000000..593a5ac426
--- /dev/null
+++ b/challenge-159/roger-bell-west/ruby/ch-1.rb
@@ -0,0 +1,52 @@
+#! /usr/bin/ruby
+
+require 'test/unit'
+
+require 'set'
+require 'prime'
+
+def lcmseries(s)
+  return s.inject {|a, b| a.lcm(b)}
+end
+
+def farey(n)
+  l=lcmseries(2.upto(n))
+  d={}
+  s=[]
+  1.upto(n) do |i|
+    m = l / i
+    0.upto(i) do |j|
+      k = m * j
+      if !d.has_key?(k) then
+        d[k]=[j,i]
+        s.push(k)
+      end
+    end
+  end
+  s.sort!
+  return s.map{|i| d[i]}
+end
+
+class TestFarey < Test::Unit::TestCase
+
+  def test_ex1
+    assert_equal([[0, 1], [1, 5], [1, 4], [1, 3], [2, 5], [1, 2],
+                  [3, 5], [2, 3], [3, 4], [4, 5], [1, 1]],
+                 farey(5))
+  end
+
+  def test_ex2
+    assert_equal([[0, 1], [1, 7], [1, 6], [1, 5], [1, 4], [2, 7],
+                  [1, 3], [2, 5], [3, 7], [1, 2], [4, 7], [3, 5],
+                  [2, 3], [5, 7], [3, 4], [4, 5], [5, 6], [6, 7],
+                  [1, 1]],
+                 farey(7))
+  end
+
+  def test_ex3
+    assert_equal([[0, 1], [1, 4], [1, 3], [1, 2], [2, 3], [3, 4],
+                  [1, 1]],
+                 farey(4))
+  end
+
+end
diff --git a/challenge-159/roger-bell-west/ruby/ch-2.rb b/challenge-159/roger-bell-west/ruby/ch-2.rb
new file mode 100755
index 0000000000..4d59457cba
--- /dev/null
+++ b/challenge-159/roger-bell-west/ruby/ch-2.rb
@@ -0,0 +1,36 @@
+#! /usr/bin/ruby
+
+require 'test/unit'
+
+require 'set'
+require 'prime'
+
+def moebius(n)
+  z=0
+  for vv in n.prime_division do
+    if vv[1] > 1 then
+      return 0
+    end
+    z += 1
+  end
+  if z % 2 == 0 then
+    return 1
+  end
+  return -1
+end
+
+class TestMoebius < Test::Unit::TestCase
+
+  def test_ex1
+    assert_equal(-1,moebius(5))
+  end
+
+  def test_ex2
+    assert_equal(1,moebius(10))
+  end
+
+  def test_ex3
+    assert_equal(0,moebius(20))
+  end
+
+end
diff --git a/challenge-159/roger-bell-west/rust/ch-1.rs b/challenge-159/roger-bell-west/rust/ch-1.rs
new file mode 100755
index 0000000000..aee5bc331d
--- /dev/null
+++ b/challenge-159/roger-bell-west/rust/ch-1.rs
@@ -0,0 +1,97 @@
+#! /bin/sh
+//usr/bin/env rustc --test $0 -o ${0}x && ./${0}x --nocapture; rm -f ${0}x ; exit
+
+use std::collections::HashMap;
+
+#[test]
+fn test_ex1() {
+    assert_eq!(
+        farey(5),
+        vec![
+            [0, 1],
+            [1, 5],
+            [1, 4],
+            [1, 3],
+            [2, 5],
+            [1, 2],
+            [3, 5],
+            [2, 3],
+            [3, 4],
+            [4, 5],
+            [1, 1]
+        ]
+    );
+}
+
+#[test]
+fn test_ex2() {
+    assert_eq!(
+        farey(7),
+        vec![
+            [0, 1],
+            [1, 7],
+            [1, 6],
+            [1, 5],
+            [1, 4],
+            [2, 7],
+            [1, 3],
+            [2, 5],
+            [3, 7],
+            [1, 2],
+            [4, 7],
+            [3, 5],
+            [2, 3],
+            [5, 7],
+            [3, 4],
+            [4, 5],
+            [5, 6],
+            [6, 7],
+            [1, 1]
+        ]
+    );
+}
+
+#[test]
+fn test_ex3() {
+    assert_eq!(
+        farey(4),
+        vec![[0, 1], [1, 4], [1, 3], [1, 2], [2, 3], [3, 4], [1, 1]]
+    );
+}
+
+fn gcd(m0: usize, n0: usize) -> usize {
+    let mut m = m0;
+    let mut n = n0;
+    while n != 0 {
+        let t = n;
+        n = m % n;
+        m = t;
+    }
+    m
+}
+
+fn lcm(m: usize, n: usize) -> usize {
+    m / gcd(m, n) * n
+}
+
+fn lcmseries(s: Vec<usize>) -> usize {
+    s.iter().fold(1, |acc, x| lcm(acc, *x))
+}
+
+fn farey(n: usize) -> Vec<[usize; 2]> {
+    let l = lcmseries((2..=n).collect::<Vec<usize>>());
+    let mut d: HashMap<usize, [usize; 2]> = HashMap::new();
+    let mut s = Vec::new();
+    for i in 1..=n {
+        let m = l / i;
+        for j in 0..=i {
+            let k = m * j;
+            if !d.contains_key(&k) {
+                d.insert(k, [j, i]);
+                s.push(k);
+            }
+        }
+    }
+    s.sort();
+    return s.iter().map(|i| d[i]).collect::<Vec<[usize; 2]>>();
+}
diff --git a/challenge-159/roger-bell-west/rust/ch-2.rs b/challenge-159/roger-bell-west/rust/ch-2.rs
new file mode 100755
index 0000000000..106b67293d
--- /dev/null
+++ b/challenge-159/roger-bell-west/rust/ch-2.rs
@@ -0,0 +1,84 @@
+#! /bin/sh
+//usr/bin/env rustc --test $0 -o ${0}x && ./${0}x --nocapture; rm -f ${0}x ; exit
+
+use std::collections::{HashMap, HashSet, VecDeque};
+use std::iter::FromIterator;
+
+#[test]
+fn test_ex1() {
+    assert_eq!(moebius(5), -1);
+}
+
+#[test]
+fn test_ex2() {
+    assert_eq!(moebius(10), 1);
+}
+
+#[test]
+fn test_ex3() {
+    assert_eq!(moebius(20), 0);
+}
+
+fn genprimes(mx: usize) -> Vec<usize> {
+    let mut primesh: HashSet<usize> = HashSet::from_iter(2..=3);
+    for i in (6..=mx).step_by(6) {
+        for j in [i - 1, i + 1] {
+            if j < mx {
+                primesh.insert(j);
+            }
+        }
+    }
+    let mut q = VecDeque::from([2, 3, 5, 7]);
+    let mut p = q.pop_front().unwrap();
+    let mr = (mx as f64).sqrt() as usize;
+    while p <= mr {
+        if primesh.contains(&p) {
+            for i in (p * p..=mx).step_by(p as usize) {
+                primesh.remove(&i);
+            }
+        }
+        if q.len() < 2 {
+            let t = q[0] + 4;
+            q.push_back(t);
+            q.push_back(t + 2);
+        }
+        p = q.pop_front().unwrap();
+    }
+    let mut primes = primesh.iter().map(|i| *i).collect::<Vec<usize>>();
+    primes.sort();
+    primes
+}
+
+fn primefactor(n: usize) -> HashMap<usize, usize> {
+    let mut f: HashMap<usize, usize> = HashMap::new();
+    let mut m = n;
+    for p in genprimes((n as f64).sqrt() as usize).iter() {
+        while m % p == 0 {
+            m /= p;
+            let en = f.entry(*p).or_insert(0);
+            *en += 1;
+        }
+        if m == 1 {
+            break;
+        }
+    }
+    if m > 1 {
+        let en = f.entry(m).or_insert(0);
+        *en += 1;
+    }
+    f
+}
+
+fn moebius(n: usize) -> isize {
+    let mut z=0;
+    for v in primefactor(n).values() {
+        if *v > 1 {
+            return 0;
+        }
+        z += 1;
+    }
+    if z % 2 == 0 {
+        return 1;
+    }
+    -1
+}
-- 
cgit 


From afb541c10466df9d9ca45c17f3056fd11a016e47 Mon Sep 17 00:00:00 2001
From: Luca Ferrari <fluca1978@gmail.com>
Date: Mon, 4 Apr 2022 10:53:44 +0200
Subject: Task 2 plperl

---
 challenge-159/luca-ferrari/postgresql/ch-2.plperl | 57 +++++++++++++++++++++++
 1 file changed, 57 insertions(+)
 create mode 100644 challenge-159/luca-ferrari/postgresql/ch-2.plperl

diff --git a/challenge-159/luca-ferrari/postgresql/ch-2.plperl b/challenge-159/luca-ferrari/postgresql/ch-2.plperl
new file mode 100644
index 0000000000..8dce608e5a
--- /dev/null
+++ b/challenge-159/luca-ferrari/postgresql/ch-2.plperl
@@ -0,0 +1,57 @@
+CREATE SCHEMA IF NOT EXISTS pwc159;
+
+/**
+testdb=> select pwc159.mobius( 5 );
+ mobius 
+--------
+     -1
+(1 row)
+
+*/
+CREATE OR REPLACE FUNCTION
+pwc159.mobius( int )
+RETURNS int
+AS $CODE$
+
+   my ( $n ) = @_;
+
+   # a routine to compute the prime
+   # factors of the given number
+   my $prime_factors = sub {
+      my ( $number ) = @_;
+      my %factors;
+
+      my $factor = 2;
+      while (  $number > 1 && $factor <= $number ) {
+            if ( $number % $factor == 0 ) {
+               $factors{ $factor }++;
+               $number /= $factor;
+            }
+            else {
+                 $factor++;
+            }
+      }
+
+      return %factors;
+   };
+
+
+   my %prime_factors = $prime_factors->( $n );
+
+   # to get the unique prime factors I have to "count"
+   # them only once per key
+   my @unique_prime_factors;
+   my $occurrencies_prime_factors = 0;
+   for ( keys %prime_factors ) {
+       push @unique_prime_factors, $_;
+       $occurrencies_prime_factors += $prime_factors{ $_ };
+   }
+
+
+   return 0 if @unique_prime_factors != $occurrencies_prime_factors;
+   return 1 if @unique_prime_factors % 2 == 0;
+   return -1;
+
+
+$CODE$
+LANGUAGE plperl;
-- 
cgit 


From d6c45c1e8fbd72ec613baff00a8214a270f3f6cb Mon Sep 17 00:00:00 2001
From: Luca Ferrari <fluca1978@gmail.com>
Date: Mon, 4 Apr 2022 11:06:28 +0200
Subject: Task 2 done in plpgsql

---
 challenge-159/luca-ferrari/postgresql/ch-2.sql | 42 ++++++++++++++++++++++++++
 1 file changed, 42 insertions(+)

diff --git a/challenge-159/luca-ferrari/postgresql/ch-2.sql b/challenge-159/luca-ferrari/postgresql/ch-2.sql
index da8824c0c2..d165df2fed 100644
--- a/challenge-159/luca-ferrari/postgresql/ch-2.sql
+++ b/challenge-159/luca-ferrari/postgresql/ch-2.sql
@@ -1 +1,43 @@
 -- Perl Weekly Challenge 159
+
+CREATE SCHEMA IF NOT EXISTS  pwc159;
+
+CREATE OR REPLACE FUNCTION
+pwc159.prime_factors( n int )
+RETURNS SETOF int
+AS $CODE$
+DECLARE
+        factor int;
+BEGIN
+        factor := 2;
+
+        WHILE ( factor <= n AND n > 1 ) LOOP
+              IF n % factor = 0 THEN
+                 n := n / factor;
+                 RETURN NEXT factor;
+              ELSE
+                factor := factor + 1;
+              END IF;
+        END LOOP;
+
+        RETURN;
+END
+$CODE$
+LANGUAGE plpgsql;
+
+
+\set n 5
+
+WITH count_prime_factors(  c, cc ) AS
+(
+        SELECT count( distinct pf ), count( pf )
+        FROM pwc159.prime_factors( :n ) pf
+)
+SELECT :n AS number,
+       CASE
+       WHEN c - cc <> 0 THEN 0
+       WHEN c % 2  = 0  THEN 1
+       ELSE -1
+       END
+
+FROM count_prime_factors;
-- 
cgit 


From 593f633c0d938cf962a5ffd4c99e4ed08acb9b99 Mon Sep 17 00:00:00 2001
From: Luca Ferrari <fluca1978@gmail.com>
Date: Mon, 4 Apr 2022 11:51:35 +0200
Subject: Blog references

---
 challenge-159/luca-ferrari/blog-1.txt | 1 +
 challenge-159/luca-ferrari/blog-2.txt | 1 +
 challenge-159/luca-ferrari/blog-3.txt | 1 +
 challenge-159/luca-ferrari/blog-4.txt | 1 +
 challenge-159/luca-ferrari/blog-5.txt | 1 +
 challenge-159/luca-ferrari/blog-6.txt | 1 +
 6 files changed, 6 insertions(+)
 create mode 100644 challenge-159/luca-ferrari/blog-1.txt
 create mode 100644 challenge-159/luca-ferrari/blog-2.txt
 create mode 100644 challenge-159/luca-ferrari/blog-3.txt
 create mode 100644 challenge-159/luca-ferrari/blog-4.txt
 create mode 100644 challenge-159/luca-ferrari/blog-5.txt
 create mode 100644 challenge-159/luca-ferrari/blog-6.txt

diff --git a/challenge-159/luca-ferrari/blog-1.txt b/challenge-159/luca-ferrari/blog-1.txt
new file mode 100644
index 0000000000..adc4af027c
--- /dev/null
+++ b/challenge-159/luca-ferrari/blog-1.txt
@@ -0,0 +1 @@
+https://fluca1978.github.io/2022/04/04/PerlWeeklyChallenge159.html#task1
diff --git a/challenge-159/luca-ferrari/blog-2.txt b/challenge-159/luca-ferrari/blog-2.txt
new file mode 100644
index 0000000000..970839190a
--- /dev/null
+++ b/challenge-159/luca-ferrari/blog-2.txt
@@ -0,0 +1 @@
+https://fluca1978.github.io/2022/04/04/PerlWeeklyChallenge159.html#task2
diff --git a/challenge-159/