use ntheory qw/factor/;
sub closest {
  my($n) = @_;
  my(@factors, @d, @t);
  # 1. Get list of factors
  @factors = factor($n);
  # 2. Turn this into an unsorted list of divisors
  @d = (1);
  while (my $p = shift @factors) {
    my $e = 1;
    while (@factors && $p == $factors[0]) { $e++; shift(@factors); }
    push @d,  @t = map { $_ * $p } @d;               # multiply through once
    push @d,  @t = map { $_ * $p } @t   for 2 .. $e; # repeat
  }
  # 3. Sort
  @d = sort {$a<=>$b} @d;
  # 4. Return the largest divisor <= sqrt n.
  $d[ $#d >> 1 ];
}