A096850 Consider iteration of the function f(x) = phi(sigma(x)) = A062401(x). Sequence gives numbers n such that the trajectory of n returns to n.
1, 2, 4, 6, 8, 12, 16, 24, 30, 48, 60, 72, 96, 128, 240, 432, 480, 576, 720, 864, 1200, 1280, 1512, 1536, 1728, 1800, 1860, 2016, 2560, 2880, 3024, 3456, 3840, 6912, 10368, 14080, 15552, 15840, 18144, 27648, 30976, 32768, 34560, 41472, 42240, 48384
Offset: 1
Keywords
Examples
Examples of cycles: {[1], [2], [4, 6], [8], [12], [16, 30, 24], [48, 60], [72, 96], [128]}.
95 => 32 => 36 => 72 => 96 => 72 => ..., therefore 72 and 96 are in the sequence.
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 1..110
Programs
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Mathematica
a = {}; f[n_] := EulerPhi[ DivisorSigma[ 1, n]]; Do[ AppendTo[a, NestWhileList[f, n, UnsameQ, All][[ -1]]]; a = Union[a], {n, 10^6}]; Take[ a, 46] (* Robert G. Wilson v, Jul 21 2004 *) -
PARI
f(n)=eulerphi(sigma(n)) is(n)=my(t=f(n),h=f(t));while(t!=h,t=f(t);h=f(f(h));if(t==n, return(1)));t==n \\ Charles R Greathouse IV, Nov 27 2013
Extensions
Edited and extended by Robert G. Wilson v, Jul 21 2004