If 10 is not a solitary number, what properties would a friend of 10 have It is of course an unsolved problem if 10 is solitary or not, but it is conjectured that it is. (See definition of friendly and solitary number on wiki: < So why is it conjectured that 10 is solitary? Wikipedia says that if 10 has a friend it is "a fairly large number". Presumably a computer search found no example. But pairs can be friends, even if they live quite far appart. An example is (24,91963648). Solely on that grounds I wouldn't conjecture it if there aren't any more reasons. I found out that a possible friend of 10 is divisible by 5 and is not divisible by 2. But that's as far as I got. Are there any other known restrictions that point to the conjecture?

There is more information in the paper 'Does ten have a friend' by Jeffrey Ward. It is available at < (see theorem 1 in that paper).