A077092 Fixed points of iteration in A077091.

0, 4, 24, 8064, 34944, 35520, 38880, 69480, 268560, 420096, 1054944, 2946560, 3054080, 5660160, 6621120, 9768960, 10264320, 25885760, 29062656, 33933312, 36484992, 38707200, 78532608, 163418112, 260601600, 458987520, 4044349440

Offset: 1

Author

Labos Elemer, Oct 31 2002

Keywords

• nonn

Comments

When iteration of f(k) = phi(sigma(k)-phi(k)) is started at various initial values, not ending in cycles and converging, it ends at these fixed points.

a(28) <= 11435212800. a(29) <= 15083274240. a(30) <= 90215424000. - Donovan Johnson, Dec 14 2009

Examples

			n=30: FixedPointList={30,32,46,20,16,22,12,8,10,6,4},end=4; n=94: FixedPointList={94,42,24},end=24. n=41708: FixedPointList={41708,26064,32352,21216,15232,8064},end=8064; n=12100: FixedPointList={12100,24000,34944},end=34944.
		

Crossrefs

Cf. A077090, A077091, A077093, A077094, A077095, A077096, A077099, A077100.

Programs

Mathematica

f[x_] := EulerPhi[DivisorSigma[1, x]-EulerPhi[x]] Do[s=NestList[f, n, 100]; s1=Part[s, 99]; s2=Part[s, 100]; If[Equal[s1, s2]&&!PrimeQ[n], Print[{n, s1}]], {n, 1, 1000}]

Extensions

a(9) corrected and a(11)-a(27) from Donovan Johnson, Dec 14 2009