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 A356548 Let S(n)=sigma(n)/3. Numbers k such that S^m(k)=k, 1/3-sociable numbers (of any order). 0

%I #16 Aug 14 2022 06:53:16

%S 120,672,7560,7680,8064,8184,8840,9600,10540,34944,36576,38080,65520,

%T 71680,75264,77748,90272,472416,510720,523776,605024,654080,1100190,

%U 1124352,14913024,16149760,27797760,33931072,34012160,459818240

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

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

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

%e 120 -> 120 so 120 is a term, a 3-perfect number.

%e 7680 -> 8184 -> 7680, a group of 2 sociable terms.

%e 7560 -> 9600 -> 10540 -> 8064 -> 8840 -> 7560, a group of 5 sociable terms.

%e 34944 -> 38080 -> 36576 -> 34944, a group of 3 sociable terms.

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

%K nonn,more

%O 1,1

%A _Michel Marcus_, Aug 11 2022

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Last modified August 14 08:37 EDT 2024. Contains 375159 sequences. (Running on oeis4.)