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

1,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..110

Example

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.

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 *)

Prog

(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

Crossrefs

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

Sequence in context: A325238 A344385 A070175 * A250270 A062847 A001013

Adjacent sequences: A096847 A096848 A096849 * A096851 A096852 A096853

Keyword

nonn

Author

Labos Elemer, Jul 16 2004

Extensions

Edited and extended by Robert G. Wilson v, Jul 21 2004

Status

approved