

A343243


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.


0



20339, 21159, 23883, 35503, 43255, 45375, 365599, 476343, 493047, 746383, 979839, 1097367, 3331135, 3816831, 3972543, 57720703, 68705247, 78376959, 3031407415, 3742563231, 3866214695
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OFFSET

1,1


COMMENTS

The numbers k such that s(k) = k are the perfect totient numbers (A082897).
a(22) > 2*10^10, if it exists.


LINKS



EXAMPLE

20339 is a term since s(20339) = 23883, s(23883) = 21159 and s(21159) = 20339.


MATHEMATICA

totSum[n_] := Plus @@ FixedPointList[EulerPhi, n]  n  1; soc3TotQ[n_] := Nest[totSum, n, 3] == n && totSum[n] != n; Select[Range[2, 10^6], soc3TotQ]


CROSSREFS



KEYWORD

nonn,more


AUTHOR



STATUS

approved



