A183016 Conjectured list of smallest terms of k-sociable cycles of order r.

6, 28, 120, 220, 496, 672, 1184, 2620, 5020, 6232, 8128, 10744, 12285, 12496, 14316, 17296, 30240, 32760, 63020, 66928, 67095, 69615, 79750, 100485, 122265, 122368, 141664, 142310, 171856, 176272, 185368, 196724, 280540, 308620, 319550

Offset: 1

Author

William Rex Marshall, Jan 08 2011

Keywords

• nonn

Comments

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

A183017(n) gives the multiplicity of the cycle with smallest term a(n).

A183018(n) gives the order of the cycle with smallest term a(n).

If examples of two or more multisociable cycles with the same smallest term exist, the smallest term is repeated in this sequence, and corresponding multiplicities listed in order of increasing size in A183017. (No such examples are known. Do any exist?)

Crossrefs

Cf. A000396, A001065, A002025, A003416, A007691, A183017 (multiplicities), A183018 (orders), A183019, A183021.