sub divisors {
  my($n,@factors) = @_;
  my $sqrtn = int(sqrt($n));

  my %all_factors;
  foreach my $f ( grep { $_ <= $sqrtn } @factors) {
    my @to_add = grep { $_ <= $sqrtn }
                 map { $f * $_ }
                 keys %all_factors;
    undef @all_factors{ $f, @to_add };
  }
  undef $all_factors{1};
  my @d = sort {$a<=>$b} keys %all_factors;
  @d, map { $_*$_ == $n ? () : int($n/$_) } reverse @d;
}