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%I #12 Nov 21 2016 16:38:22
%S 16,18,21,24,25,27,28,30,31,33,34,35,37,38,39,40,44,45,46,47,51,53,55,
%T 58,59,61,65,71,83,86,89,109,131,137,149,900,1116,1152,1156,1200,1236,
%U 1260,1300,1320,1380,1386,1410,1428,1458,1488,1500,1518,1524,1533,1536
%N Initial values for f(x) = phi(sigma(x)) such that iteration of f ends in a cycle of length 3.
%H Charles R Greathouse IV, <a href="/A095953/b095953.txt">Table of n, a(n) for n = 1..10000</a>
%e n=900: trajectory={900, 2160, 1920, [1536, 1200, 1860], 1536, ...}.
%t g[n_] := EulerPhi[ DivisorSigma[1, n]]; f[n_] := f[n] = Block[{lst = NestWhileList[g, n, UnsameQ, All ]}, -Subtract @@ Flatten[ Position[lst, lst[[ -1]]]]]; Select[ Range[1540], f[ # ] == 3 &] (* _Robert G. Wilson v_, Jul 14 2004 *)
%t fcl3Q[n_]:=Length[FindTransientRepeat[NestList[EulerPhi[DivisorSigma[1,#]]&,n,100],3][[2]]]==3; Select[Range[1600],fcl3Q] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Nov 21 2016 *)
%o (PARI) f(x)=eulerphi(sigma(x))
%o is(n)=my(t=f(n), h=f(t)); while(t!=h, t=f(t); h=f(f(h))); h=f(h); t!=h && t==f(f(h)) \\ _Charles R Greathouse IV_, Nov 22 2013
%Y Cf. A000010, A000203, A095952, A096887, A096526, A095954, A096888, A096889, A096890, A095955, A095956.
%K nonn
%O 1,1
%A _Labos Elemer_, Jul 13 2004
%E More terms from _Robert G. Wilson v_, Jul 14 2004
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