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A097006
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Consider the function f(x)=sigma(phi(x))=A062402(x) iterated with initial value n!; a[n] is the path-length of trajectory.
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0
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1, 1, 2, 2, 2, 5, 6, 5, 10, 10, 17, 49, 91
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| The path length is the total number of transient and recurrent terms.
After 12000 iterations, f(13!) reaches 583880633503221176888439640142607059743547704176558111997560422400000.
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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.
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MAPLE
| f[n_] := DivisorSigma[1, EulerPhi[n]]; g[n_] := Length[ NestWhileList[ f, n, UnsameQ, All]] - 1; Table[ g[n! ], {n, 12}] (from Robert G. Wilson v Jul 23 2004)
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CROSSREFS
| Cf. A000203, A000010, A062401, A000142, A097005.
Sequence in context: A190846 A066835 A123953 * A033306 A136347 A145876
Adjacent sequences: A097003 A097004 A097005 * A097007 A097008 A097009
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KEYWORD
| nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Jul 22 2004
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EXTENSIONS
| Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 23 2004
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