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I have a question.

In the OEIS (Known friendly numbers) is following information:

The sequence is not known to be complete up to 372, since there are many small numbers, including 10, 14, 15 and 20, which have not been proved to be solitary. If any other numbers up to 372 are friendly, the smallest corresponding values of m are > 10^30.

How we can calculate it up to m = $10^{30}$?

The classic algorithm is much slower.

I was looking for some publications but unfortunately did not find anything.

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    Impressing indeed! – 2017-01-23
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    I do not know how it works exactly, but instead of testing all pairs, we have to concentrate on the sigma function for various prime factorizations. There must be plenty of properties waiting to be exploited. – 2017-01-23

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