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A076640
a(1)=1, a(n) = a(n-phi(n)) + 1.
3
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
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
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
KEYWORD
nonn,changed
AUTHOR
Benoit Cloitre, Oct 23 2002
STATUS
approved