A095953 Initial values for f(x) = phi(sigma(x)) such that iteration of f ends in a cycle of length 3.

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

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

n=900: trajectory={900, 2160, 1920, [1536, 1200, 1860], 1536, ...}.

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A000010, A000203, A095952, A096887, A096526, A095954, A096888, A096889, A096890, A095955, A095956.

Sequence in context: A328736 A348143 A161874 * A084800 A065426 A308607

Adjacent sequences: A095950 A095951 A095952 * A095954 A095955 A095956

Keyword

nonn

Author

Labos Elemer, Jul 13 2004

Extensions

More terms from Robert G. Wilson v, Jul 14 2004

Status

approved