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A095953
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Initial values for f(x) = phi(sigma(x)) such that iteration of f ends in a cycle of length 3.
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13
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16, 18, 21, 24, 25, 27, 28, 30, 31, 33, 34, 35, 37, 38, 39, 40, 44, 45, 46, 47, 51, 53, 55, 58, 59, 61, 65, 71, 83, 86, 89, 109, 131, 137, 149, 900, 1116, 1152, 1156, 1200, 1236, 1260, 1300, 1320, 1380, 1386, 1410, 1428, 1458, 1488, 1500, 1518, 1524, 1533, 1536
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OFFSET
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1,1
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LINKS
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EXAMPLE
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n=900: trajectory={900, 2160, 1920, [1536, 1200, 1860], 1536, ...}.
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MATHEMATICA
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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 *)
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 *)
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PROG
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(PARI) f(x)=eulerphi(sigma(x))
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
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CROSSREFS
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Cf. A000010, A000203, A095952, A096887, A096526, A095954, A096888, A096889, A096890, A095955, A095956.
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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