(I suppose only positive numbers otherwise multiply it with 2)

The following is just a variation of the code I recently used:

(I love branch and bound! :)

9! = 362880 possible combinations¹ are checked in a recursive function.

#!perl
use strict;
use warnings;

my @digits = 1..9;

my @number;
my $maxlevel=10;

my %count_hash;
my $count=0;

append_digit();

print "count: $count\n";

print join "\n", sort { $a <=>$b } keys %count_hash;


sub append_digit {

  my $level = scalar @number;

  my $number= join "", @number;
  
  if ( $level and
       ! grep {$number % $_} @number
     ) {
    $count++;
    print "$count: $number\n" unless $count %100;
    $count_hash{$number} = undef;
  }

  for my $digit (@digits) {
    return if $level > $maxlevel;                 #  for testing only
    next if $digit ~~ @number;

    push @number, $digit;
    append_digit();
    pop @number;
  }
}
[download]