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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 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

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