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A073407 Let phi_m(x) denote the Euler totient function applied m times to x. Sequence gives the minimum number of iterations m such that phi_m(n) divides n. 1
1, 1, 2, 1, 3, 1, 3, 1, 3, 2, 4, 1, 4, 2, 4, 1, 5, 1, 4, 2, 4, 3, 5, 1, 5, 3, 4, 2, 5, 3, 5, 1, 5, 4, 5, 1, 5, 3, 5, 2, 6, 3, 5, 3, 5, 4, 6, 1, 5, 4, 6, 3, 6, 1, 6, 2, 5, 4, 6, 3, 6, 4, 5, 1, 6, 4, 6, 4, 6, 4, 6, 1, 6, 4, 6, 3, 6, 4, 6, 2, 5, 5, 7, 3, 7, 4, 6, 3, 7, 4, 6, 4, 6, 5, 6, 1, 7, 4, 6, 4, 7, 5, 7, 3, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

It seems that sum(k=1, n, a(k)) is asymptotic to C*n*log(n) with C>1.

EXAMPLE

phi(22) -> 10, phi(10) -> 4, phi(4) -> 2 and 2 divides 22. Hence 3 iterations are needed and a(22) = 3.

MATHEMATICA

a[n_] := Module[{c = 0, k = n}, While[c == 0 || !Divisible[n, k], k = EulerPhi[k]; c++]; c]; Array[a, 105] (* Amiram Eldar, Jul 10 2019 *)

PROG

(PARI) a(n) = if(n<0, 0, c=1; s=n; while(n%eulerphi(s)>0, s=eulerphi(s); c++); c)

CROSSREFS

Cf. A000010, A019294.

Sequence in context: A226859 A025820 A109704 * A049994 A135732 A322584

Adjacent sequences:  A073404 A073405 A073406 * A073408 A073409 A073410

KEYWORD

easy,nonn,changed

AUTHOR

Benoit Cloitre, Aug 23 2002

STATUS

approved

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Last modified July 22 14:44 EDT 2019. Contains 325222 sequences. (Running on oeis4.)