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%I #5 Apr 08 2021 22:11:30
%S 20339,21159,23883,35503,43255,45375,365599,476343,493047,746383,
%T 979839,1097367,3331135,3816831,3972543,57720703,68705247,78376959,
%U 3031407415,3742563231,3866214695
%N Sociable totient numbers of order 3: numbers k such that s(s(s(k))) = k, but s(k) != k, where s(k) = A092693(k) is the sum of iterated phi function.
%C The numbers k such that s(k) = k are the perfect totient numbers (A082897).
%C a(22) > 2*10^10, if it exists.
%e 20339 is a term since s(20339) = 23883, s(23883) = 21159 and s(21159) = 20339.
%t totSum[n_] := Plus @@ FixedPointList[EulerPhi, n] - n - 1; soc3TotQ[n_] := Nest[totSum, n, 3] == n && totSum[n] != n; Select[Range[2, 10^6], soc3TotQ]
%Y Cf. A000010, A082897, A092693, A286233.
%K nonn,more
%O 1,1
%A _Amiram Eldar_, Apr 08 2021