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

Terms

a(0) =120a(1) =672a(2) =7560a(3) =7680a(4) =8064a(5) =8184a(6) =8840a(7) =9600a(8) =10540a(9) =34944a(10) =36576a(11) =38080a(12) =65520a(13) =71680a(14) =75264a(15) =77748a(16) =90272a(17) =472416a(18) =510720a(19) =523776a(20) =605024a(21) =654080a(22) =1100190a(23) =1124352a(24) =14913024a(25) =16149760a(26) =27797760a(27) =33931072a(28) =34012160a(29) =459818240