

A334685


Start with n, and successively apply phi, phi, sigma, phi, phi, sigma, phi, ... until reaching 1; a(n) is the number of steps needed (phi = A000010, sigma = A000203); or a(n) = 1 if 1 is never reached.


5



0, 1, 2, 2, 5, 2, 5, 5, 5, 5, 8, 5, 8, 5, 8, 8, 11, 5, 8, 8, 8, 8, 8, 8, 11, 8, 8, 8, 11, 8, 11, 11, 11, 11, 11, 8, 11, 8, 11, 11, 14, 8, 11, 11, 11, 8, 11, 11, 11, 11, 14, 11, 14, 8, 14, 11, 11, 11, 14, 11, 14, 11, 11, 14, 14, 11, 11, 14, 11, 11, 14, 11, 14, 11, 14, 11, 14, 11, 14, 14, 14, 14, 14, 11, 14, 11, 14, 14
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OFFSET

1,3


COMMENTS

Created following a suggestion from R. J. Mathar in an attempt to understand A032452.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..25000
L. Alaoglu and P. Erdős, A conjecture in elementary number theory, Bull. Amer. Math. Soc. 50 (1944), 881882.


EXAMPLE

The trajectory of n=11 is 11, 10, 4, 7, 6, 2, 3, 2, 1, 1, 1, ..., which takes eight steps to reach 1, so a(11) = 8.


MATHEMATICA

Array[1 + Length@ NestWhile[Append[#1, If[#2 == 0, DivisorSigma[1, #1[[1]]], EulerPhi@ #1[[1]] ]] & @@ {#, Mod[Length@ #, 3]} &, {#}, Last[#] > 1 &] &, 80] (* Michael De Vlieger, May 09 2020 *)


PROG

(PARI) a(n) = { for (k=0, oo, if (n==1, return (k), k%3==2, n=sigma(n), n=eulerphi(n))) } \\ Rémy Sigrist, May 09 2020


CROSSREFS

Cf. A000010, A000203, A032452, A334686, A334523, A334725.
Sequence in context: A171889 A171868 A292146 * A340694 A101910 A162784
Adjacent sequences: A334682 A334683 A334684 * A334686 A334687 A334688


KEYWORD

nonn


AUTHOR

N. J. A. Sloane, May 08 2020


STATUS

approved



