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TASK #1 - Pernicious Numbers
Write a script to permute first 10 Pernicious Numbers.
A pernicious number is a positive integer which has prime number of ones
in its binary representation.
The first pernicious number is 3 since binary representation of 3 =
(11) and 1 + 1 = 2, which is a prime.
Expected Output
3, 5, 6, 7, 9, 10, 11, 12, 13, 14
MY NOTES: ok. Pretty easy. pernicious(n) = isprime(countones(binary(n)))
TASK #2 - Weird Number
You are given number, $n > 0.
Write a script to find out if the given number is a Weird Number.
According to Wikipedia, it is defined as:
The sum of the proper divisors (divisors including 1 but not itself) of
the number is greater than the number, but no subset of those divisors
sums to the number itself.
Example 1:
Input: $n = 12
Output: 0
Since the proper divisors of 12 are 1, 2, 3, 4, and 6, which sum to 16;
but 2 + 4 + 6 = 12.
Example 2:
Input: $n = 70
Output: 1
As the proper divisors of 70 are 1, 2, 5, 7, 10, 14, and 35; these sum
to 74, but no subset of these sums to 70.
MY NOTES: ok. Handle "sum of subsets of these items" by noting that
each item may be present or absent, so have a counting loop from 0..
2**(nitems)-1 and compute the sum of just those items selected by the
binary bits of the count that are 1.
Bonus: I added a "tabulate" facility (eg. run with --tabulate 5 to
see the first 5 Weird numbers).
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