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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.
6

%I #8 Nov 29 2013 14:52:42

%S 1,2,4,6,8,12,16,24,30,48,60,72,96,128,240,432,480,576,720,864,1200,

%T 1280,1512,1536,1728,1800,1860,2016,2560,2880,3024,3456,3840,6912,

%U 10368,14080,15552,15840,18144,27648,30976,32768,34560,41472,42240,48384

%N 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.

%H Charles R Greathouse IV, <a href="/A096850/b096850.txt">Table of n, a(n) for n = 1..110</a>

%e Examples of cycles: {[1], [2], [4, 6], [8], [12], [16, 30, 24], [48, 60], [72, 96], [128]}.

%e 95 => 32 => 36 => 72 => 96 => 72 => ..., therefore 72 and 96 are in the sequence.

%t 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 *)

%o (PARI) f(n)=eulerphi(sigma(n))

%o 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

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

%K nonn

%O 1,2

%A _Labos Elemer_, Jul 16 2004

%E Edited and extended by _Robert G. Wilson v_, Jul 21 2004