A077094 Numbers k such that iterating phi(sigma(k)-phi(k)) starting from k leads to the fixed point 4.

4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 25, 26, 27, 28, 30, 32, 33, 34, 35, 38, 39, 44, 45, 46, 49, 51, 54, 55, 56, 57, 58, 62, 63, 65, 68, 70, 77, 85, 87, 91, 93, 95, 99, 104, 111, 119, 121, 129, 134, 143, 145, 153, 158, 161, 169, 189, 205, 209, 215, 221, 245

Offset: 1

Author

Labos Elemer, Oct 31 2002

Keywords

• nonn

Comments

Probably this sequence is finite, with 92 terms of which the last is 6241.

Examples

			n=6241: FixedPointList={6241,104,54,32,20,16,22,12,8,10,6,4}, end=4.
		

Links

• Sean A. Irvine, Table of n, a(n) for n = 1..92

Crossrefs

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

Cf. A077090, A077091, A077092, A077093, A077095, 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}]
f4[n_]:=FixedPoint[EulerPhi[DivisorSigma[1,#]-EulerPhi[#]]&,n,50]==4; Select[Range[250],f4] (* Harvey P. Dale, May 01 2021 *)

Extensions

Definition corrected by Harvey P. Dale, May 01 2021