A095954 Initial values for f(x)=phi(sigma(x)) such that iteration of f ends in a cycle of length 6.

784, 800, 882, 912, 960, 972, 1008, 1024, 1050, 1072, 1080, 1089, 1104, 1168, 1204, 1216, 1225, 1232, 1248, 1250, 1264, 1281, 1290, 1296, 1302, 1308, 1332, 1350, 1352, 1360, 1368, 1371, 1372, 1392, 1400, 1407, 1416, 1425, 1440, 1456, 1461, 1464, 1467

Offset

1,1

Links

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

Example

n=882:trajectory={882, 1296, 3300, [2880, 3024, 3840, 3456, 2560, 1800], 2880, ..}

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[1500], f[ # ] == 6 &] (* Robert G. Wilson v, Jul 14 2004 *)

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!=(h=f(h)) && t!=(h=f(h)) && t==f(f(f(h))) \\ Charles R Greathouse IV, Nov 23 2013

Crossrefs

Cf. A000010, A000203, A095952, A096887, A095953, A096526, A096888, A096889, A096890, A095955, A095956.

Sequence in context: A158399 A007243 A146978 * A351476 A257355 A187935

Adjacent sequences: A095951 A095952 A095953 * A095955 A095956 A095957

Keyword

nonn

Author

Labos Elemer, Jul 13 2004

Status

approved