@LongListOfIntegers = grep $_ &1, @LongListOfIntegers;

foreach my $i1 ( 0 .. $#LongListOfIntegers) {
    use integer;
    my $v = $LongListOfIntegers[ $i1 ];
    ($v & $_) == 1 and undef $MatchedIntegers{$i1}{$_} 
        foreach @LongListOfIntegers[ $i1+1 .. $#LongListOfIntegers ];
}