A097003 - OEIS

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].

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, 92, 59, 37, 54, 1

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OFFSET

0,3

COMMENTS

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.

Glossary: t+c = total count of transient+cycle terms, t = count of transient terms

Sequence 1: A062401 is iterated t+c is computed => this sequence

Sequence 2: A062402 is iterated t+c is computed => A097004

Sequence 3: A062401 is iterated t is computed => A096994

Sequence 4: A062402 is iterated t is computed => A096995

LINKS

Table of n, a(n) for n=0..31.

EXAMPLE

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;

MATHEMATICA

EulerPhi[DivisorSigma[1, x]] itef[x_, len_] :=NestList[fs, x, len] Table[Length[Union[itef[2^w, 20]]], {w, 1, 256}]

CROSSREFS