This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A076640 #21 Nov 11 2024 22:38:47
%S A076640 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 A076640 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 A076640 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 A076640 a(1)=1, a(n) = a(n-phi(n)) + 1.
%H A076640 T. D. Noe, <a href="/A076640/b076640.txt">Table of n, a(n) for n=1..10000</a>
%F A076640 It seems that for n large enough: log(n) < (1/n)*sum(k=1, n, a(k)) < log(n)+log(log(n)).
%F A076640 a(n) = A053475(n) - 1.
%F A076640 For n = p^k, p prime (A000040), k >= 0, a(n) = A000005(n). - _Ctibor O. Zizka_, Nov 09 2024
%t A076640 Table[Length@ NestWhileList[# - EulerPhi@ # &, n, # > 0 &] - 1, {n, 105}] (* _Michael De Vlieger_, Jul 04 2016 *)
%o A076640 (PARI) a(n)=if(n<2,1,a(n-eulerphi(n))+1)
%Y A076640 Cf. A000005, A000040, A053475.
%K A076640 nonn
%O A076640 1,2
%A A076640 _Benoit Cloitre_, Oct 23 2002