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A073408 Let cophi_m(x) denotes the cototient function applied m times to x (cophi(x)=x-phi(x)). Sequence gives the minimum number of iterations m such that cophi_m(n) divides n. 1
1, 1, 1, 1, 2, 1, 1, 1, 3, 1, 2, 1, 3, 2, 1, 1, 4, 1, 3, 2, 4, 1, 2, 1, 4, 1, 3, 1, 5, 1, 1, 2, 5, 2, 4, 1, 5, 3, 3, 1, 6, 1, 4, 2, 5, 1, 2, 1, 6, 2, 4, 1, 6, 3, 3, 3, 6, 1, 5, 1, 5, 2, 1, 2, 6, 1, 5, 3, 6, 1, 4, 1, 6, 3, 5, 2, 7, 1, 3, 1, 7, 1, 6, 4, 6, 2, 4, 1, 7, 2, 5, 3, 6, 2, 2, 1, 6, 4, 6, 1, 7, 1, 4, 2, 7 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,5

LINKS

Antti Karttunen, Table of n, a(n) for n = 2..16385

FORMULA

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

EXAMPLE

cophi(10) -> 6, cophi(6) -> 4, cophi(4) -> 2 and 2 divides 10. Hence 3 iterations are needed and a(10) = 3.

MATHEMATICA

Table[Length@ NestWhileList[# - EulerPhi@ # &, n, Or[# == n, ! Divisible[n, #]] &, 1, 12] - 1, {n, 2, 106}] (* Michael De Vlieger, Dec 22 2017 *)

PROG

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

CROSSREFS

Cf. A019294, A051953.

Sequence in context: A316557 A032436 A280274 * A120454 A321648 A316431

Adjacent sequences:  A073405 A073406 A073407 * A073409 A073410 A073411

KEYWORD

easy,nonn

AUTHOR

Benoit Cloitre, Aug 23 2002

STATUS

approved

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Last modified July 20 01:38 EDT 2019. Contains 325168 sequences. (Running on oeis4.)