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%I #9 Aug 17 2017 11:55:41
%S 1,2,3,5,6,8,10,13,15,12,14,17,15,17,24,28,24,24,25,22,24,29,43,47,27,
%T 27,27,37,44,30,51,56,38,38,41,41,40,60,40,45,69,43,43,45,52,46,51,54,
%U 50,53,52,86,56,58,54,58,61,86,63,72,63,64,61,67,67,108,68,102,77,71,76
%N Number of powers of 2 in the iteration-sequence when A051953 (cototient function) is repeatedly applied starting with n!.
%C Unlike the analogous sequence with A000005, the powers of 2 which emerge are consecutive iterates.
%e n=7, initial value=7!=5040, the successive iterates when cototient function (A051953) is repeatedly applied are: {5040,3888,2592,1728,1152,768,512,256,128,64,32,16,8,4,2,1,0}. Between the initial segment and terminal 0, ten powers of 2 emerge: 512,...,1. Thus a(7)=10.
%t a[n_] := Module[{x = n!}, While[ ! IntegerQ[Log[2, x]], x = x - EulerPhi[x];]; Log[2, x] + 1]; (* Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 12 2006 *)
%Y Cf. A051953, A053475.
%K nonn
%O 1,2
%A _Labos Elemer_, Feb 24 2000
%E More terms from Sam Handler (sam_5_5_5_0(AT)yahoo.com), Sep 12 2006
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