A183026 Conjectured list of smallest members of fully k-sociable cycles of order r.

1, 6, 12, 28, 48, 112, 120, 160, 192, 448, 496, 672, 1984, 7560, 7680, 8128, 12288, 28672, 30240, 32760, 34944, 65520, 126976, 196608, 458752, 472416, 520192, 523776, 786432, 859320, 1100190, 1835008, 2031616, 2096640, 2178540, 8126464

Offset: 1

Author

William Rex Marshall, Jan 08 2011

Keywords

• nonn

Comments

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.

A183027(n) gives the multiplicity of the cycle with smallest term a(n).

A183028(n) gives the order of the cycle with smallest term a(n).

If examples of two or more fully 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 A183027. (No such examples are known. Do any exist?)

Crossrefs

Cf. A000203, A000396, A007691, A183027 (multiplicities), A183028 (orders), A183029.