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Example: 72 has the following divisors: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72. The median (middle) divisors are 8 and 9. Provided we already have the prime factors of a number x, what would be an algorithm to find these two divisors? What would be the complexity of that algorithm? x would typically be a number with lots of prime factors, e.g. "Highly composite numbers".

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    $\begingroup$ This is effectively a multiplicative version of partition problem, so I doubt a particularly efficient algorithm exists. Since primes are relatively dense, one may be able to prove that this problem is NP-hard. $\endgroup$ Commented Jun 24 at 11:27
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    $\begingroup$ See mathoverflow.net/q/419722 for a possible ILP-based approach and discussion of its shortcomings. $\endgroup$ Commented Jun 24 at 11:49

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