First, thanks for the good work. I go back and reread this sometimes, and somehow manage, mostly, not to get bitten, being satisfied rereading all the excellent ideas. It was loads of fun at the time, and still tickles my fancy even now.

In your code 1, I find this a little odd:

$d[($#d-1)>>1];
[download]

If there are 3 divisors, then $#d == 2, and $#d -1 == 1, and 1>>1 == 0. So instead of the middle divisor, we get 1. If there is 1 divisor, we get -1 (I think), which perhaps doesn't matter, giving the last element by Perl magic.

But overall, I would agree a priori that something well written that returns a list of divisors will be faster than something returning a list of prime factors, which then have to be recombined to get divisors. Unless there is a very large list of divisors, and a very short list of prime factors, but that is an edge case, I think.

Thanks for refreshing one of my favorite threads.

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