powerfree_divisors.pl

#!/usr/bin/perl

# Author: Trizen
# Date: 13 September 2023
# https://github.com/trizen

# Generate the k-powerfree divisors of a given number.

# See also:
#   https://oeis.org/A048250

use 5.036;
use ntheory qw(:all);

sub powerfree_divisors ($n, $k = 2) {

    my @d = (1);

    foreach my $pp (factor_exp($n)) {
        my ($p, $e) = @$pp;

        $e = vecmin($e, $k - 1);

        my @t;
        my $r = 1;
        for (1 .. $e) {
            $r = mulint($r, $p);
            push @t, map { mulint($r, $_) } @d;
        }
        push @d, @t;
    }

    return sort { $a <=> $b } @d;
}

say join(', ', powerfree_divisors(5040, 2));    # squarefree divisors
say join(', ', powerfree_divisors(5040, 3));    # cubefree divisors

__END__
1, 2, 3, 5, 6, 7, 10, 14, 15, 21, 30, 35, 42, 70, 105, 210
1, 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, 630, 1260