A356548 Let S(n)=sigma(n)/3. Numbers k such that S^m(k)=k, 1/3-sociable numbers (of any order).

120, 672, 7560, 7680, 8064, 8184, 8840, 9600, 10540, 34944, 36576, 38080, 65520, 71680, 75264, 77748, 90272, 472416, 510720, 523776, 605024, 654080, 1100190, 1124352, 14913024, 16149760, 27797760, 33931072, 34012160, 459818240

Offset

1,1

Comments

It appears that, for initial i=660880440, the sequence x->S(x) diverges.

Barring such cases, the next 3 terms would be 775898880, 874897408 and 1476304896.

Links

Table of n, a(n) for n=1..30.

Example

120 -> 120 so 120 is a term, a 3-perfect number.
7680 -> 8184 -> 7680, a group of 2 sociable terms.
7560 -> 9600 -> 10540 -> 8064 -> 8840 -> 7560, a group of 5 sociable terms.
34944 -> 38080 -> 36576 -> 34944, a group of 3 sociable terms.

Crossrefs

Subsequences: A005820 (3-perfect), A113546 (1/3-sociable numbers of order 1 and 2).

Sequence in context: A342923 A292365 A306373 * A113546 A281771 A166069

Adjacent sequences: A356545 A356546 A356547 * A356549 A356550 A356551

Keyword

nonn,more

Author

Michel Marcus, Aug 11 2022

Status

approved