cp's OEIS Frontend

A097003 Function A062402[x]=phi[sigma[x]] is iterated. a(n) is the number of distinct terms arising in the trajectory of 2^n; a(n)=t(n)+c(n)=t+c, where t is the number of transient terms, c is the number of recurrent terms [in the terminal cycle].

%I A097003 #5 Oct 15 2013 22:32:33
%S A097003 1,1,2,1,3,4,4,1,3,4,10,3,3,11,16,1,7,10,13,25,10,5,79,58,99,100,94,
%T A097003 92,59,37,54,1
%N A097003 Function A062402[x]=phi[sigma[x]] is iterated. a(n) is the number of distinct terms arising in the trajectory of 2^n; a(n)=t(n)+c(n)=t+c, where t is the number of transient terms, c is the number of recurrent terms [in the terminal cycle].
%C A097003 Concerning this sequence and A097004, A096994, A096995: in all 4 cases the initial value is 2^n and a certain function is iterated. They differ either in the function or in what is computed for that iteration.
%C A097003 Glossary: t+c = total count of transient+cycle terms, t = count of transient terms
%C A097003 Sequence 1: A062401 is iterated t+c is computed => this sequence
%C A097003 Sequence 2: A062402 is iterated t+c is computed => A097004
%C A097003 Sequence 3: A062401 is iterated t is computed => A096994
%C A097003 Sequence 4: A062402 is iterated t is computed => A096995
%e A097003 n=13: 2^n=8192, trajectory ={8192, 10584, 8640, 8064, 6144, [3456, 2560, 1800, 2880, 3024, 3840], 3456, 2560, ..}, t+c=a(13)=5+6=11;
%t A097003 EulerPhi[DivisorSigma[1, x]] itef[x_, len_] :=NestList[fs, x, len] Table[Length[Union[itef[2^w, 20]]], {w, 1, 256}]
%Y A097003 Cf. A000010, A000203, A062402, A096852.
%K A097003 nonn
%O A097003 0,3
%A A097003 _Labos Elemer_, Jul 21 2004