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.

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

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

Table of n, a(n) for n=1..21.

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

Cf. A000010, A082897, A092693, A286233.

Sequence in context: A250451 A031825 A234631 * A156408 A045815 A182294

Adjacent sequences: A343240 A343241 A343242 * A343244 A343245 A343246

Keyword

nonn,more

Author

Amiram Eldar, Apr 08 2021

Status

approved