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A181627 Number of iterations of phi(n) if n is a perfect totient number. 0
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A365399 A267530 A050292 * A071521 A204330 A225553
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

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Last modified April 23 02:53 EDT 2024. Contains 371906 sequences. (Running on oeis4.)