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

Author

Labos Elemer, Jul 13 2004

Keywords

• nonn

Examples

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

Links

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

Crossrefs

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

Programs

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 *)

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

Extensions

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