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A077092 Fixed points of iteration in A077091. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

When iteration of f[]=Phi[Sigma[]-Phi[]] 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. [From Donovan Johnson, Dec 14 2009]

LINKS

Table of n, a(n) for n=1..27.

EXAMPLE

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.

MAPLE

with(numtheory): P:=proc(q) local n; for n from 0 to q do

if phi(sigma(n)-phi(n))=n then print(n); fi; od; end: P(10^10); # Paolo P. Lava, Jun 18 2014

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}]

CROSSREFS

Cf. A077090-A077100.

Sequence in context: A279240 A279110 A077093 * A092435 A058230 A162187

Adjacent sequences:  A077089 A077090 A077091 * A077093 A077094 A077095

KEYWORD

nonn

AUTHOR

Labos Elemer, Oct 31 2002

EXTENSIONS

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

STATUS

approved

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Last modified April 13 00:17 EDT 2021. Contains 342934 sequences. (Running on oeis4.)