You can save more time and space by using a string of '1's & '0's, and a bit more still using a bitstring.

sub buk1 {
    my $lights = '1' x ( 20_000 );

    for my $gap ( 2 .. 20_000 ) {
        for( my $o = $gap; $o <= 20_000; $o += $gap ) {
            substr($lights, $o, 1) = substr($lights, $o, 1) eq '0' ? '
+1' : '0';
        }
    }

    $answers{ buk1 } = join ', ', grep{ substr( $lights, $_, 1 ) } 1 .
+. 20_000;
}

sub buk2 {
    my $lights = "\xFF" x ( 20_001 / 8 );

    for my $gap ( 2 .. 20_000 ) {
        for( my $o = $gap; $o < 20_000; $o += $gap ) {
            vec( $lights, $o, 1 ) = ~vec( $lights, $o, 1 );
        }
    }

    $answers{ buk2 } = join ', ', grep{ vec( $lights, $_, 1 ) } 1 .. 2
+0_000;
}

P:\test>junk
            Rate   duckyd2    duckyd tanktalus       buk      buk2
duckyd2   1.96/s        --       -1%      -53%      -66%      -69%
duckyd    1.99/s        1%        --      -53%      -66%      -68%
tanktalus 4.20/s      114%      111%        --      -28%      -33%
buk       5.82/s      197%      193%       39%        --       -7%
buk2      6.27/s      220%      215%       49%        8%        --
Comparing buk1 and buk2
Comparing buk2 and duckyd
Comparing duckyd and duckyd2
Comparing duckyd2 and tanktalus
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