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A097006 Consider the function f(x)=sigma(phi(x))=A062402(x) iterated with initial value n!; a(n) is the path-length of trajectory. 0
1, 1, 2, 2, 2, 5, 6, 5, 10, 10, 17, 49, 91 (list; graph; refs; listen; history; text; internal format)
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

AUTHOR

Labos Elemer, Jul 22 2004

EXTENSIONS

Edited by Robert G. Wilson v, Jul 23 2004

STATUS

approved

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Last modified September 22 17:05 EDT 2018. Contains 315270 sequences. (Running on oeis4.)