A004607 Infinitary sociable numbers (smallest member of cycle).

1026, 10098, 10260, 12420, 41800, 45696, 100980, 241824, 448800, 512946, 685440, 830568, 4938136, 6732000, 9424800, 12647808, 13959680, 14958944, 17878998, 25581600, 28158165, 32440716, 36072320, 55204500, 74062944

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice
• more

Comments

If n = Product p_i^a_i, d = Product p_i^c_i is an infinitary divisor of n if each c_i has a zero bit in its binary representation everywhere that the corresponding a_i does.

From Amiram Eldar, Mar 25 2023: (Start)

Analogous to A003416 with the sum of the aliquot infinitary divisors function (A126168) instead of A001065.

Only cycles of length greater than 2 are here. Cycles of length 1 correspond to infinitary perfect numbers (A007357), and cycles of length 2 correspond to infinitary amicable pairs (A126169 and A126170).

The corresponding cycles are of lengths 4, 4, 4, 6, 4, 4, 4, 4, 11, 6, 4, 6, 4, 11, 6, 23, 4, 4, 85, 4, 4, 4, 4, 4, 4, ...

It is conjectured that there are no missing terms in the data, but it was not proven. For example, it is not known that the infinitary aliquot sequence that starts at 840 does not reach 840 again (see A361421). (End)

Links

• Graeme L. Cohen, On an integer's infinitary divisors, Math. Comp. 54 (189) (1990) 395-411.
• J. O. M. Pedersen, Tables of Aliquot Cycles.
• J. O. M. Pedersen, Tables of Aliquot Cycles. [Via Internet Archive Wayback-Machine]
• J. O. M. Pedersen, Tables of Aliquot Cycles. [Cached copy, pdf file only]

Crossrefs

Cf. A001065, A003416, A007357, A126168, A126169, A126170, A361421.