An amicable chain of natural numbers of length n is an ordered n-tuple of distinct naturals (a_1,...a_n) such that the sum of the proper divisors of a_i equals a_{i+1}, for all i mod n. Is it known if there are arbitrarily long amicable chains? The longest I can find is here: http://demonstrations.wolfram.com/ChainsOfAmicableNumbers/
2026-04-13 16:10:59.1776096659
Arbitrarily long amicable chains
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