4 files changed, 281 insertions, 0 deletions
diff --git a/challenge-169/pokgopun/go/ch-1.go b/challenge-169/pokgopun/go/ch-1.go
new file mode 100644
index 0000000000..fa6ae0e57c
--- /dev/null
+++ b/challenge-169/pokgopun/go/ch-1.go
@@ -0,0 +1,105 @@
+/*
+Write a script to generate first 20 Brilliant Numbers.
+
+Brilliant numbers are numbers with two prime factors of the same length.
+
+The number should have exactly two prime factors, i.e. it’s the product of two primes of the same length.
+*/
+package main
+
+import (
+	"fmt"
+	"log"
+	"math"
+	"os"
+	"sort"
+	"strconv"
+	"strings"
+)
+
+func main() {
+	var n uint = 20
+	if len(os.Args) > 1 {
+		_, err := fmt.Sscanf(os.Args[1], "%d", &n)
+		if err != nil {
+			log.Fatal(err)
+		}
+	}
+	fmt.Println(newBrlntNum(n))
+}
+
+func newBrlntNum(n uint) (bn brlntNum) {
+	if n < 1 {
+		log.Fatal("number must be greater than 0")
+	}
+	bn.n = int(n)
+	k := 99
+	for len(bn.vals) < bn.n {
+		bn.buildPrime(k)
+		bn.pgroup = [][]int{[]int{}}
+		bn.vals = []int{}
+		var i, j int
+		j++
+		for {
+			if len(strconv.Itoa(bn.plist[i])) == j {
+				bn.pgroup[j-1] = append(bn.pgroup[j-1], bn.plist[i])
+				i++
+				if i >= len(bn.plist) {
+					break
+				}
+			} else {
+				j++
+				bn.pgroup = append(bn.pgroup, []int{})
+			}
+		}
+		for l := 0; l < j; l++ {
+			for p := 0; p < len(bn.pgroup[l]); p++ {
+				for q := p; q < len(bn.pgroup[l]); q++ {
+					bn.vals = append(bn.vals, bn.pgroup[l][p]*bn.pgroup[l][q])
+				}
+			}
+		}
+		k = 10*k + 9
+	}
+	sort.SliceStable(bn.vals, func(i, j int) bool {
+		return bn.vals[i] < bn.vals[j]
+	})
+	//fmt.Println(bn.pgroup)
+	return bn
+}
+
+type brlntNum struct {
+	n      int
+	pmap   []bool
+	plist  []int
+	pgroup [][]int
+	vals   []int
+}
+
+func (bn brlntNum) String() string {
+	var b strings.Builder
+	for i := 0; i < bn.n; i++ {
+		b.WriteString(", " + strconv.Itoa(bn.vals[i]))
+	}
+	return b.String()[2:]
+}
+
+func (bn *brlntNum) buildPrime(n int) {
+	bn.pmap = make([]bool, int(n)+1)
+	for i := 2; i <= n; i++ {
+		bn.pmap[i] = true
+	}
+	for i := 2; float64(i) <= math.Sqrt(float64(n)); i++ {
+		j := i * i
+		for j <= n {
+			bn.pmap[j] = false
+			j += i
+		}
+	}
+	bn.plist = []int{}
+	for i := 2; i < len(bn.pmap); i++ {
+		if bn.pmap[i] {
+			bn.plist = append(bn.plist, i)
+		}
+	}
+}
diff --git a/challenge-169/pokgopun/go/ch-2.go b/challenge-169/pokgopun/go/ch-2.go
new file mode 100644
index 0000000000..19c93edbe4
--- /dev/null
+++ b/challenge-169/pokgopun/go/ch-2.go
@@ -0,0 +1,147 @@
+/*
+Write a script to generate first 20 Achilles Numbers. Please checkout wikipedia for more information.
+
+An Achilles number is a number that is powerful but imperfect (not a perfect power). Named after Achilles, a hero of the Trojan war, who was also powerful but imperfect.
+
+A positive integer n is a powerful number if, for every prime factor p of n, p^2 is also a divisor.
+
+A number is a perfect power if it has any integer roots (square root, cube root, etc.).
+*/
+package main
+
+import (
+	"fmt"
+	"log"
+	"math"
+	"math/big"
+	"os"
+	"strconv"
+	"strings"
+)
+
+func main() {
+	var n uint = 20
+	if len(os.Args) > 1 {
+		_, err := fmt.Sscanf(os.Args[1], "%d", &n)
+		if err != nil {
+			log.Fatal(err)
+		}
+	}
+	fmt.Println(newAchlsNum(n))
+}
+
+func newAchlsNum(n uint) (an achlsNum) {
+	if n < 1 {
+		log.Fatal("number must be greater than 0")
+	}
+	// build enough prime numbers to check n numbers of achilles
+	an.n = int(n)
+	k := 2 * an.n
+	if k < 3 {
+		k = 3
+	}
+	an.buildPrime(k)
+	// First archilles is 1st prime power of three multiplied by square of 2nd prime => 72
+	i := an.plist[0] * an.plist[0] * an.plist[0] * an.plist[1] * an.plist[1]
+	an.vals = append(an.vals, i)
+	i++
+	for len(an.vals) < an.n {
+		// pontential achilles would never be prime, fast-forward to the one that is not
+		for big.NewInt(int64(i)).ProbablyPrime(0) {
+			i++
+		}
+		// check if it is achilles and store or try next if it is not
+		if an.isAchls(i) {
+			an.vals = append(an.vals, i)
+		}
+		i++
+	}
+	//fmt.Println(an.plist)
+	return an
+}
+
+type achlsNum struct {
+	n     int
+	pmap  []bool
+	plist []int
+	vals  []int
+}
+
+func (an achlsNum) isAchls(n int) bool {
+	// achilles is powerful but with imperfect power
+	m := make(map[int]int)
+	var d int
+	max := n
+	for _, d = range an.plist {
+		if d*d >= max {
+			break
+		}
+		for n%d == 0 {
+			m[d]++
+			n /= d
+		}
+		// a prime factor happens less than twice is not powerful
+		if m[d] != 0 && m[d] < 2 {
+			return false
+		}
+	}
+	// a remainder is a prime factor happens once, thus is not powerful
+	if n > 1 {
+		return false
+	}
+	// having less than two prime factors is not powerful
+	l := len(m)
+	if l < 2 {
+		return false
+	}
+	// check for imperfect power
+	// prime factor powers having a gcd other than 1 indicate a perfect power
+	var min int
+	// find the minimum of prime factor powers
+	for _, v := range m {
+		if min == 0 {
+			min = v
+		} else if min > v {
+			min = v
+		}
+	}
+	// check if there a valid gcd other than 1 up to min, if so, it idicates a perfect power thus not achilles
+	for gcd := 2; gcd <= min; gcd++ {
+		var sum int
+		for _, v := range m {
+			sum += v % gcd
+		}
+		if sum == 0 {
+			return false
+		}
+	}
+	// without any further objections, it is achilles
+	return true
+}
+
+func (an achlsNum) String() string {
+	var b strings.Builder
+	for i := 0; i < an.n; i++ {
+		b.WriteString(", " + strconv.Itoa(an.vals[i]))
+	}
+	return b.String()[2:]
+}
+func (an *achlsNum) buildPrime(n int) {
+	an.pmap = make([]bool, int(n)+1)
+	for i := 2; i <= n; i++ {
+		an.pmap[i] = true
+	}
+	for i := 2; float64(i) <= math.Sqrt(float64(n)); i++ {
+		j := i * i
+		for j <= n {
+			an.pmap[j] = false
+			j += i
+		}
+	}
+	an.plist = []int{}
+	for i := 2; i < len(an.pmap); i++ {
+		if an.pmap[i] {
+			an.plist = append(an.plist, i)
+		}
+	}
+}
diff --git a/challenge-169/pokgopun/perl/ch-1.pl b/challenge-169/pokgopun/perl/ch-1.pl
new file mode 100644
index 0000000000..7ac35d6056
--- /dev/null
+++ b/challenge-169/pokgopun/perl/ch-1.pl
@@ -0,0 +1,13 @@
+use strict;
+use warnings;
+use Math::Prime::Util qw/is_semiprime factor/;
+#
+# By its definition, 1st Brilliant number is square of 1st prime numbers
+# => 2*2 = 4
+my ($i,$count) = (4,0);
+print($i) && $i++ && $count++;
+{
+	print ", $i" if is_semiprime($i) && eval(join(" - ", map{ length } factor $i ))==0 && $count++; 
+	$i++ && redo if $count < 20;
+	print "\n";
+}
diff --git a/challenge-169/pokgopun/perl/ch-2.pl b/challenge-169/pokgopun/perl/ch-2.pl
new file mode 100644
index 0000000000..7dc4f8acfd
--- /dev/null
+++ b/challenge-169/pokgopun/perl/ch-2.pl
@@ -0,0 +1,16 @@
+use strict;
+use warnings;
+use Math::Prime::Util qw/is_prime factor gcd/;
+#
+# By its definition, 1st Achilles number is made of first two primes, their powers are greater than 1 but with gcd=1 
+# => 2*2*2*3*3 = 72
+my ($i,$count) = (72,0);
+print($i) && $i++ && $count++;
+{
+	redo if is_prime $i && $i++;
+	my %factor;
+	$factor{$_}++ foreach factor $i;
+	print ", $i" if keys(%factor) > 1 && !scalar(grep{$_ < 2} values %factor) && gcd(values %factor)==1 && $count++;
+	$i++ && redo if $count < 20;
+	print "\n";
+}