A096862 Function A062402(x)=sigma(phi(x)) is iterated. Starting with n, a(n) is the count of distinct terms arising during this 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].

1, 2, 1, 2, 3, 2, 2, 3, 3, 3, 4, 2, 2, 3, 1, 2, 4, 3, 5, 2, 2, 4, 3, 2, 3, 2, 5, 1, 5, 2, 3, 4, 3, 4, 4, 2, 4, 5, 4, 4, 5, 2, 6, 3, 4, 3, 4, 4, 6, 3, 5, 4, 7, 5, 5, 4, 4, 5, 5, 3, 3, 4, 4, 5, 3, 3, 4, 5, 5, 4, 4, 3, 3, 4, 5, 4, 3, 4, 3, 5, 6, 5, 5, 4, 5, 6, 6, 5, 4, 4, 3, 5, 3, 4, 3, 5, 3, 6, 3, 5, 8, 5, 4, 3, 3

Offset

1,2

Links

Table of n, a(n) for n=1..105.

Example

n=256: list={256,255,255}, transient=t=1, cycle=c=1, a(256)=t+c=2.

Mathematica

gf[x_] :=DivisorSigma[1, EulerPhi[x]] gite[x_, hos_] :=NestList[gf, x, hos] Table[Length[Union[gite[w, 1000]]], {w, 1, 256}]

Crossrefs

Cf. A062401, A062402, A095955, A096859-A096866.

Sequence in context: A216763 A112759 A309971 * A029309 A049819 A284566

Adjacent sequences: A096859 A096860 A096861 * A096863 A096864 A096865

Keyword

nonn

Author

Labos Elemer, Jul 21 2004

Status

approved