The solution by Athanasius is already very nice and succinct; it can find all 548 solutions twice as fast (31 seconds instead of 65) if the tests are performed for each digit rather than after all digits have been hashed:

#!/usr/bin/perl -w

use strict;
use warnings;

my $count = 0;
my $start = time;

OUTER:
for my $n (1 .. 987_654_321) {

  my %digits;

  map { next OUTER if !$_ or $digits{$_}++ or $n % $_ } split //, $n;

  printf "#%d is %d\n", ++$count, $n;

  ($count == 548) and printf "Time:  %d sec\n", time - $start;
}
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