TL;DR

On with TASK #2 from The Weekly Challenge #159. Enjoy!

The challenge

You are given a positive number $n.

Write a script to generate the Moebius Number for the given number. Please refer to wikipedia page for more informations.

Example 1:

Input: $n = 5
Output: -1

Example 2:

Input: $n = 10
Output: 1

Example 3:

Input: $n = 20
Output: 0

The questions

This challenge is a sibling of PWC150 - Square-free Integer, with the exception that this time we’re told that we have to consider only positive numbers. I mean… integer numbers, right?

The solution

We’re adapting the solution from PWC150 - Square-free Integer, just to remain on the lazy side:

#!/usr/bin/env perl
use v5.24;
use warnings;
use experimental 'signatures';
no warnings 'experimental::signatures';

say $_, ' ', moebius_number($_) for (@ARGV ? @ARGV : (1 .. 10));

sub moebius_number ($n) {
   return 0 unless $n % 4;
   ($n, my $n_divisors) = $n % 2 ? ($n, 0) : ($n / 2, 1);
   my $divisor = 3;
   while ($n >= $divisor) {
      if ($n % $divisor == 0) {
         ++$n_divisors;
         $n /= $divisor;
         return 0 unless $n % $divisor;
      }
      $divisor += 2; # go through odd candidates only
   }
   return 1 - 2 * ($n_divisors % 2);
}

And the same goes for Raku:

#!/usr/bin/env raku
use v6;
sub MAIN (*@args) { put $_, ' ', möbius-number($_) for @args}

sub möbius-number ($n is copy) {
   return 0 if $n %% 4;
   ($n, my $n-divisors) = $n %% 2 ?? (($n / 2).Int, 1) !! ($n, 0);
   my $divisor = 3;
   while $n >= $divisor {
      if $n %% $divisor {
         ++$n-divisors;
         $n = ($n / $divisor).Int;
         return 0 if $n %% $divisor;
      }
      $divisor += 2; # go through odd candidates only
   }
   return 1 - 2 * ($n-divisors % 2);
}

The case for divisibility by 2 is handled specially just to be able to increment the $divisor variable by 2 instead of by 1. Apart from this, we’re sticking to the definition in the Wikipedia page, returning 0 whenever we find a square in the divisors, or using the even/odd count of prime factors to figure out the right value to return.

Stay safe folks!