%I A096859
%S A096859 1,1,2,2,2,2,3,1,2,3,3,1,3,2,2,3,3,4,2,2,4,2,2,3,4,2,4,4,2,3,4,4,4,5,4,
%T A096859 3,5,4,4,4,2,5,3,4,4,4,4,2,4,3,4,6,5,5,4,5,5,4,4,2,4,5,3,4,4,3,5,4,5,3,
%U A096859 4,2,4,4,3,3,5,3,5,3,4,4,4,3,4,5,5,3,4,3,3,3,5,3,5,2,6,4,3,7,5,3,3,3,5
%N A096859 Function A062401(x)=phi(sigma(x))=f(x) is iterated. Starting with n, 
               a(n) is the count of distinct terms arising in trajectory; a(n)=t(n)+c(n)=t+c, 
               where t=number of transient terms, c=number of recurrent terms (in 
               the terminal cycle).
%e A096859 n=255: list={255,144,360,288,[432,480],432,.},t=transient=4,c=cycle=2, 
               a[255]=t+c=6;
%e A096859 n=244: list={244,180,144,360,288,[432,480],432,..},t=5,c=2,a[244]=7.
%t A096859 fs[x_] :=EulerPhi[DivisorSigma[1, x]] itef[x_, len_] :=NestList[fs, x, 
               len] Table[Length[Union[itef[2^w, 20]]], {w, 1, 256}] (len=20 at 
               n<=256 is suitable)
%Y A096859 Cf. A062401, A062402, A095955, A096860-A096864.
%Y A096859 Sequence in context: A067089 A090872 A063473 this_sequence A005086 A157372 
               A020649
%Y A096859 Adjacent sequences: A096856 A096857 A096858 this_sequence A096860 A096861 
               A096862
%K A096859 nonn
%O A096859 1,3
%A A096859 Labos E. (labos(AT)ana.sote.hu), Jul 21 2004