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
Examples
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.
Programs
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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 *)
Extensions
Edited by Robert G. Wilson v, Jul 23 2004
Comments