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

Author

Amiram Eldar, Apr 08 2021

Keywords

• nonn
• more

Comments

The numbers k such that s(k) = k are the perfect totient numbers (A082897).

a(22) > 2*10^10, if it exists.

Examples

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

Crossrefs

Cf. A000010, A082897, A092693, A286233.

Programs

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]