A096998 Consider iteration of the function f(x) = sigma(phi(x)) = A062402(x). Sequence lists the numbers k such that the trajectory of k returns to k.
1, 3, 7, 12, 15, 28, 31, 60, 72, 124, 168, 195, 252, 255, 744, 1240, 1512, 1651, 2418, 2520, 3066, 3844, 4092, 4800, 5080, 5376, 6045, 6138, 6552, 9906, 9920, 10200, 12264, 20440, 30855, 36792, 46228, 58968, 60984, 65535, 67963, 81880, 122640
Offset: 1
Keywords
Examples
96 => 63 => 91 => 195 => 252 => 195 => ..., therefore 195 and 252 are in the sequence.
Programs
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Mathematica
a = {}; f[n_] := DivisorSigma[1, EulerPhi[ n]]; Do[ AppendTo[ a, NestWhileList[f, n, UnsameQ, All][[ -1]]]; a = Union[a], {n, 10^6}]; Take[ a, 43] (* Robert G. Wilson v, Jul 21 2004 *)
Extensions
Edited, corrected and extended by Robert G. Wilson v, Jul 21 2004