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

Author

Labos Elemer, Jul 16 2004

Keywords

• nonn

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

Crossrefs

Cf. A062401, A095952-A095956, A096887-A096890, A096849-A096851.

Programs

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