squarefree_almost_primes_in_range.pl

#!/usr/bin/perl

# Daniel "Trizen" Șuteu
# Date: 10 March 2021
# https://github.com/trizen

# Generate squarefree k-almost prime numbers in range [a,b]. (not in sorted order)

# See also:
#   https://en.wikipedia.org/wiki/Almost_prime

use 5.020;
use ntheory qw(:all);
use experimental qw(signatures);

sub divceil ($x, $y) {    # ceil(x/y)
    (($x % $y == 0) ? 0 : 1) + divint($x, $y);
}

sub squarefree_almost_primes ($A, $B, $k, $callback) {

    $A = vecmax($A, pn_primorial($k));

    sub ($m, $lo, $k) {

        my $hi = rootint(divint($B, $m), $k);

        if ($lo > $hi) {
            return;
        }

        if ($k == 1) {

            $lo = vecmax($lo, divceil($A, $m));

            if ($lo > $hi) {
                return;
            }

            forprimes {
                $callback->(mulint($m, $_));
            } $lo, $hi;

            return;
        }

        foreach my $p (@{primes($lo, $hi)}) {
            __SUB__->(mulint($m, $p), $p+1, $k-1);
        }
    }->(1, 2, $k);
}

# Generate squarefree 5-almost primes in the range [3000, 10000]

my $k    = 5;
my $from = 3000;
my $upto = 10000;

my @arr; squarefree_almost_primes($from, $upto, $k, sub ($n) { push @arr, $n });

my @test = grep { is_almost_prime($k, $_) && is_square_free($_) } $from..$upto;   # just for testing
join(' ', sort { $a <=> $b } @arr) eq join(' ', @test) or die "Error: not equal!";

say join(', ', @arr);