A096526 Initial values for f(x)=phi(sigma(x)) such that iteration of f ends in a cycle of length 4.

324, 400, 484, 490, 530, 544, 576, 630, 660, 672, 684, 690, 714, 722, 750, 756, 768, 770, 772, 777, 780, 792, 804, 810, 819, 828, 832, 833, 840, 841, 846, 852, 858, 864, 868, 870, 872, 876, 888, 892, 901, 906, 910, 918, 920, 924, 930, 936, 940, 948, 952

Offset

1,1

Links

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

Example

n=324: trajectory=324, 660, [576, 1512, 1280, 864], 576, ...}

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[1000], f[ # ] == 4 &] (* 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==f(f(h)) \\ Charles R Greathouse IV, Nov 22 2013

Crossrefs

Cf. A000010, A000203, A095952, A096887, A095953, A095954, A096888, A096889, A096890, A095955, A095956.

Sequence in context: A088214 A117550 A045287 * A111278 A241502 A014792

Adjacent sequences: A096523 A096524 A096525 * A096527 A096528 A096529

Keyword

nonn

Author

Labos Elemer, Jul 13 2004

Status

approved