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].

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, 95, 93, 60, 38, 55, 2

Offset

0,2

Links

Table of n, a(n) for n=0..32.

Example

n=13: 2^n=8192, trajectory ={8192,8191,26208,[20440],.. }, a[13]=3+1=4 with 3 transients and one recurrent term.

Mathematica

EulerPhi[DivisorSigma[1, x]] itef[x_, len_] :=NestList[fs, x, len] Table[Length[Union[itef[2^w, 1000]]], {w, 1, 256}]

Crossrefs

Cf. A000010, A000203, A062402, A096852, A096857.

Sequence in context: A272831 A290076 A289626 * A324343 A328474 A369065

Adjacent sequences: A097001 A097002 A097003 * A097005 A097006 A097007

Keyword

nonn,more

Author

Labos Elemer, Jul 21 2004

Status

approved