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%I #15 Aug 22 2019 10:01:26
%S 1,1,2,2,2,5,6,5,10,10,17,49,91
%N Consider the function f(x)=sigma(phi(x))=A062402(x) iterated with initial value n!; a(n) is the path-length of trajectory.
%C The path length is the total number of transient and recurrent terms.
%C After 12000 iterations, f(13!) reaches 583880633503221176888439640142607059743547704176558111997560422400000.
%e 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.
%t 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 *)
%Y Cf. A000203, A000010, A062401, A000142, A097005.
%K nonn,more
%O 0,3
%A _Labos Elemer_, Jul 22 2004
%E Edited by _Robert G. Wilson v_, Jul 23 2004
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