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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
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OFFSET
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0,3
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COMMENTS
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The path length is the total number of transient and recurrent terms.
After 12000 iterations, f(13!) reaches 583880633503221176888439640142607059743547704176558111997560422400000.
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LINKS
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EXAMPLE
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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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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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