cp's OEIS Frontend

A097004 Function A062402(x)=phi(sigma(x)) is iterated. Starting with 2^n, the n-th power of 2, a(n) is the count of distinct terms arising in trajectory; 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 A097004 #8 Aug 26 2019 03:17:59
%S A097004 1,2,2,3,2,4,5,5,2,4,5,11,4,4,12,17,2,8,11,14,26,11,6,80,59,100,101,
%T A097004 95,93,60,38,55,2
%N A097004 Function A062402(x)=phi(sigma(x)) is iterated. Starting with 2^n, the n-th power of 2, a(n) is the count of distinct terms arising in trajectory; 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].
%e A097004 n=13: 2^n=8192, trajectory ={8192,8191,26208,[20440],.. }, a[13]=3+1=4 with 3 transients and one recurrent term.
%t A097004 EulerPhi[DivisorSigma[1, x]] itef[x_, len_] :=NestList[fs, x, len] Table[Length[Union[itef[2^w, 1000]]], {w, 1, 256}]
%Y A097004 Cf. A000010, A000203, A062402, A096852, A096857.
%K A097004 nonn,more
%O A097004 0,2
%A A097004 _Labos Elemer_, Jul 21 2004