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A076640 a(1)=1, a(n) = a(n-phi(n)) + 1. 3

%I #16 Jul 04 2016 11:05:49

%S 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,

%T 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,

%U 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

%N a(1)=1, a(n) = a(n-phi(n)) + 1.

%H T. D. Noe, <a href="/A076640/b076640.txt">Table of n, a(n) for n=1..10000</a>

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

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

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

%Y A053475(n) - 1.

%K nonn

%O 1,2

%A _Benoit Cloitre_, Oct 23 2002

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