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 A053034 #14 Nov 20 2017 23:23:35
%S A053034 2,3,5,7,10,13,17,20,24,32,36,40,50,55,59,63,72,78,87,101,103,114,107,
%T A053034 112,135,151,160,167,164,188,179,184,208,219,220,230,260,241,266,273,
%U A053034 261,298,311,313,321,338,342,340,367,377,389,374,410,410,438,436,457
%N A053034 Length of sequence when A051953 (cototient function) is repeatedly applied starting with n!.
%C A053034 The iteration is much slower than the analog for the divisor function; this sequence is not monotonic, cf. A053475.
%F A053034 a(n)-1 is the smallest number such that Nest[cototient, n!, a(n)]=0, the fixed point.
%e A053034 n=8: initial value = 8! = 40320; the successive iterates when cototient is iterated are {40320, 31104, 20736, 13824, 9216, 6144, 4096, 2048, 1024, 512, 256, 128, 64, 32, 16, 8, 4, 2, 1, 0}. Observe the parameters: length=20, cototient was applied 19 times, number of initial non-powers of 2 is 6 and 0 is the 7th, while 13 terminal powers of 2 did arise: 4096, ..., 2, 1.
%t A053034 a[n_] := Module[{c = 1, x = n!}, While[x != 0, x = x - EulerPhi[x]; c++;]; c]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 12 2006 *)
%Y A053034 Cf. A051953, A053475.
%K A053034 nonn
%O A053034 1,1
%A A053034 _Labos Elemer_, Feb 24 2000
%E A053034 More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 12 2006