Hi,

Pardon me for asking what must be a stupid question. I suppose I'm getting the notation wrong.

Regarding the amicable pair:

22559194686624505630=2*5*7*23*61*99643*2305266221
26660358080018237666=2*7*13*159773*523681*1750751

The factors of 22559194686624505630 do not sum up to 2666035808001823766, and the factors of 26660358080018237666 do not sum up to 22559194686624505630. What, then, makes this pair amicable?

You need to sum up all proper divisors of a number, not just factors: https://en.wikipedia.org/wiki/Aliquot_sum

To quickly check that it's indeed an amicable pair:
http://www.wolframalpha.com/input/?i=sigma(22559194686624505630)-22559194686624505630
http://www.wolframalpha.com/input/?i=sigma(26660358080018237666)-26660358080018237666

I see. Thanks!

Is there, then, an easy way to list all the proper divisors of these numbers? (But yes, I can see why you choose to list only the factors.)

I see. Thanks!

Is there, then, an easy way to list all the proper divisors of these numbers? (But yes, I can see why you choose to list only the factors.)

There is a formula to calculate sum of all proper divisors based on factorization: https://en.wikipedia.org/wiki/Divisor_function#Properties
For your case, s(22559194686624505630) = (2+1)*(5+1)*(7+1)*(23+1)*(61+1)*(99643+1)*(2305266221+1) - 22559194686624505630 = 26660358080018237666