A076640 a(1)=1, a(n) = a(n-phi(n)) + 1.

1, 2, 2, 3, 2, 4, 2, 4, 3, 5, 2, 5, 2, 5, 3, 5, 2, 6, 2, 6, 4, 6, 2, 6, 3, 6, 4, 6, 2, 7, 2, 6, 3, 7, 3, 7, 2, 7, 4, 7, 2, 8, 2, 7, 5, 7, 2, 7, 3, 8, 3, 7, 2, 8, 4, 7, 5, 8, 2, 8, 2, 7, 5, 7, 3, 8, 2, 8, 4, 8, 2, 8, 2, 8, 4, 8, 3, 9, 2, 8, 5, 9, 2, 9, 5, 8, 3, 8, 2, 9, 3, 8, 4, 8, 3, 8, 2, 8, 5, 9, 2, 9, 2, 8, 6

Offset

1,2

Links

T. D. Noe, Table of n, a(n) for n=1..10000

Formula

It seems that for n large enough: log(n) < (1/n)*sum(k=1, n, a(k)) < log(n)+log(log(n)).

Mathematica

Table[Length@ NestWhileList[# - EulerPhi@ # &, n, # > 0 &] - 1, {n, 105}] (* Michael De Vlieger, Jul 04 2016 *)

Prog

(PARI) a(n)=if(n<2, 1, a(n-eulerphi(n))+1)

Crossrefs

A053475(n) - 1.

Sequence in context: A144373 A086292 A335708 * A326198 A324105 A328871

Adjacent sequences: A076637 A076638 A076639 * A076641 A076642 A076643

Keyword

nonn

Author

Benoit Cloitre, Oct 23 2002

Status

approved