%I A053039
%S A053039 0,1,2,4,5,7,9,12,14,11,13,16,14,16,23,27,23,23,24,21,23,28,42,46,26,26,
%T A053039 26,36,43,29,50,55,37,37,40,40,39,59,39,44,68,42,42,44,51,45,50,53,49,
%U A053039 52,51,85,55,57,53,57,60,85,62,71,62,63,60,66,66,107,67,101,76,70,75,77
%N A053039 Exponent of largest power of 2 which appears in the cototient-iteration 
               started with n!.
%C A053039 If the exponent is a(n), then the number of powers of 2 in the iteration-chain 
               is 1+a(n), the maximal 2-power is 2^a(n) and the number of iterations 
               (until fixed state) performed on these 2-powers is a(n).
%e A053039 For n = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 and starting the iteration of A051593 
               with n!, the first powers of 2 which appear are 1, 2, 4, 16, 32, 
               128, 512, 4096, 16384, 2048 and the corresponding exponents are a(n) 
               = 0, 1, 2, 4, 5, 7, 9, 12, 14, 11.
%o A053039 (PARI) cototient(x)= x - eulerphi(x) FunctionIterate(f,x,t)= {local(retval); 
               retval = vector(0); while(x!=t, x = eval(concat(f,"(x)")); retval 
               = concat(retval,x)); retval;} A053039(x) = {local(li,fa,retval); 
               count = 0; li = concat([x! ],FunctionIterate("cototient", x!, 0)); 
               for(i=1,#li, fa = factor(li[i]); if(((matsize(fa)[1] == 1) && (fa[1,
               1] == 2)),retval = fa[1,2]; break)); retval} for(i=1,72,print1(A053039(i),
               ", ")) - Olaf Voss (richyfourtythree(AT)yahoo.com), Feb 21 2008
%Y A053039 Cf. A051593, A053475, A053038.
%Y A053039 Sequence in context: A007818 A158618 A000788 this_sequence A027861 A062428 
               A056833
%Y A053039 Adjacent sequences: A053036 A053037 A053038 this_sequence A053040 A053041 
               A053042
%K A053039 nonn
%O A053039 1,3
%A A053039 Labos E. (labos(AT)ana.sote.hu), Feb 24 2000
%E A053039 More terms from Olaf Voss (richyfourtythree(AT)yahoo.com), Feb 21 2008