A097006 Consider the function f(x)=sigma(phi(x))=A062402(x) iterated with initial value n!; a(n) is the path-length of trajectory.

1, 1, 2, 2, 2, 5, 6, 5, 10, 10, 17, 49, 91

Offset

0,3

Comments

The path length is the total number of transient and recurrent terms.

After 12000 iterations, f(13!) reaches 583880633503221176888439640142607059743547704176558111997560422400000.

Links

Table of n, a(n) for n=0..12.

Example

n=10: 10!=3628800; the trajectory is 3628800, 2972970, 2221560, 1915992, 1768767, 2877420, [1965840, 2227680, 1310680, 1591200, 1277874, 1307124, 1110488, 2010960, 1488032, 1981496, 2239920], [1965840, ...], ...; thus a(10)=17, with 6 transient and 11 recurrent states.

Mathematica

f[n_] := DivisorSigma[1, EulerPhi[n]]; g[n_] := Length[ NestWhileList[ f, n, UnsameQ, All]] - 1; Table[ g[n! ], {n, 12}] (* Robert G. Wilson v, Jul 23 2004 *)

Crossrefs

Cf. A000203, A000010, A062401, A000142, A097005.

Sequence in context: A214787 A066835 A123953 * A033306 A136347 A279515

Adjacent sequences: A097003 A097004 A097005 * A097007 A097008 A097009

Keyword

nonn,more

Author

Labos Elemer, Jul 22 2004

Extensions

Edited by Robert G. Wilson v, Jul 23 2004

Status

approved