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

1,1

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

Table of n, a(n) for n=1..25.

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.

Sequence in context: A291508 A371982 A031530 * A361811 A221008 A282254

Adjacent sequences: A004604 A004605 A004606 * A004608 A004609 A004610

Keyword

nonn,nice,more

Author

N. J. A. Sloane

Status

approved