%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, 1/3sociable 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 3perfect 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 (3perfect), A113546 (1/3sociable numbers of order 1 and 2).
%K nonn,more
%O 1,1
%A _Michel Marcus_, Aug 11 2022
