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

1,1

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

Table of n, a(n) for n=1..64.

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.

Formula

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

Mathematica

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

Crossrefs

Cf. A000010, A082897, A053478, A049108.

Sequence in context: A365399 A267530 A050292 * A071521 A204330 A225553

Adjacent sequences: A181624 A181625 A181626 * A181628 A181629 A181630

Keyword

nonn,more

Author

Peter Luschny, Nov 02 2010

Extensions

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

More terms from Amiram Eldar, Apr 14 2023

Status

approved