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

Author

Michel Marcus, Aug 11 2022

Keywords

• nonn
• more

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.

Examples

			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).