use strict;
my $MAX = 20001;
my @bulbs;
$bulbs[$_] = 0 for ( 0..$MAX );   # use 1 and 0 for display purposes

# Try goes thru the integers, Switching the bulbs.
TRY: for my $try ( 1..$MAX ) {
  # switch by multiples;
  MULTIPLE: for my $i ( 1..$MAX ) {
     my $m = $i*$try;
     next TRY if ( $m > $MAX );
        # a not works nicely here     
        # if you don't plan to print your array
     $bulbs[$m] = $bulbs[$m] == 1 ? 0 : 1;
  }
}

print "\n\n";
for my $n ( 1..$MAX ) {
  printf "Bulb %5d is ON\n", $n if ( $bulbs[$n] ); 
}