A181627 Number of iterations of phi(n) if n is a perfect totient number.

2, 3, 4, 4, 5, 5, 6, 7, 6, 8, 7, 8, 8, 7, 8, 10, 11, 11, 11, 11, 9, 10, 12, 10, 14, 13, 11, 16, 14, 12, 16, 17, 13, 14, 19, 15, 20, 16, 17, 18, 18, 19, 24, 19, 20, 21, 22, 29, 32, 28, 30, 22, 29, 23, 30, 32, 24, 25, 31, 35, 26, 34, 35, 27

Offset: 1

Author

Peter Luschny, Nov 02 2010

Keywords

• nonn
• more

Comments

Let phi^{i} denote the i-th iteration of phi. a(n) is the smallest integer k such that phi^{k}(n) = 1 and Sum_{1<=i<=a(n)} phi^{i}(n) = n.

Links

• Paul Loomis, Michael Plytage and John Polhill, Summing up the Euler phi function, The College Mathematics Journal, Vol. 39, No. 1, Jan. 2008, pp. 34-42.
• Peter Luschny, Sequences related to Euler's totient function.

Crossrefs

Cf. A000010, A082897, A053478, A049108.

Programs

Mathematica

lst = (* get list from A082897 *); f[n_] := Length@ FixedPointList[ EulerPhi@ # &, n] - 2; f@# & /@ lst (* Robert G. Wilson v, Nov 06 2010 *)

Formula

a(n) = A049108(A082897(n)) - 1. - Amiram Eldar, Apr 14 2023

Extensions

More terms from Robert G. Wilson v, Nov 06 2010

More terms from Amiram Eldar, Apr 14 2023