A077095 Numbers k such that iterating phi(sigma(k)-phi(k)) starting from k leads to the fixed point 24.

24, 42, 69, 74, 75, 82, 86, 94, 115, 125, 133, 155, 185, 187, 203, 289, 299, 323, 341, 361, 377, 437, 1681

Offset: 1

Author

Labos Elemer, Oct 31 2002

Keywords

• nonn

Comments

Probably this sequence is finite, with 23 terms of which the last is 1681.

Examples

			n=1641: FixedPointList={1681,82,42,24}, end=24.
		

Crossrefs

Cf. A000010 (phi), A000203 (sigma).

Cf. A077090, A077091, A077092, A077093, A077094, A077096.

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]&&Equal[s1, 4], Print[{n, s1}]], {n, 1, 1000000}]
fp24Q[n_]:=FixedPoint[EulerPhi[DivisorSigma[1,#]-EulerPhi[#]]&,n,20]==24; Select[ Range[1700],fp24Q] (* Harvey P. Dale, Mar 12 2023 *)