cp's OEIS Frontend

A fully k-sociable (or fully multisociable) cycle of order r consists of r distinct positive integers such that the sum of all the divisors of each is equal to k times the next term in the cycle, with k a fixed positive integer.

A183024(n) gives the multiplicity of the cycle with largest term a(n).

A183025(n) gives the order of the cycle with largest term a(n).

If examples of two or more fully multisociable cycles with the same largest term exist, the largest term is repeated in this sequence, and corresponding multiplicities listed in order of increasing size in A183024. (No such examples are known. Do any exist?)

a(8)=189 and a(78)=222339630960 are the largest terms of mixed parity cycles, and a(78) is the largest term of a fully 4-sociable cycle of order 34 (the longest known cycle).