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

Author

Benoit Cloitre, Oct 23 2002

Keywords

• nonn

Links

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

Crossrefs

Cf. A000005, A000040, A053475.

Programs

Mathematica

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

PARI

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

Formula

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

a(n) = A053475(n) - 1.

For n = p^k, p prime (A000040), k >= 0, a(n) = A000005(n). - Ctibor O. Zizka, Nov 09 2024