A066939 Numbers n such that phi(phi(n)) + sigma(sigma(n)) - phi(sigma(n)) - sigma(phi(n)) = phi(n) + sigma(n).

13954, 106899, 307835, 783201, 979731, 2980255, 9266817, 18479215, 49062925, 109044425, 114029313, 120914101, 185480686, 218223299, 347941741, 429365395, 466423743, 492508289, 610803875, 895938847, 993189741, 1093958383

Offset

1,1

Links

Table of n, a(n) for n=1..22.

Example

For n = 13954, phi(phi(n)) + sigma(sigma(n)) - phi(sigma(n)) - sigma(phi(n)) = phi(6976) + sigma(20934) - phi(20934) - sigma(6976) = 3456 + 45396 - 6972 - 13970 = 27910 = 6976 + 20934 = phi(n) + sigma(n), so 13954 is in the sequence.

Mathematica

g[x_] := Module[{a, b, c, d, e, f}, a=EulerPhi[x]; b=DivisorSigma[1, x]; c=EulerPhi[a]; d=DivisorSigma[1, b]; e=EulerPhi[b]; f=DivisorSigma[1, a]; a+b==c+d-e-f]; Do[If[g[n]==True, Print[n]], {n, 1, 10^6}]

Crossrefs

Cf. A000010, A000203, A066850, A066945, A066946.

Sequence in context: A118464 A031666 A031819 * A215150 A215944 A248999

Adjacent sequences: A066936 A066937 A066938 * A066940 A066941 A066942

Keyword

nonn

Author

Joseph L. Pe, Jan 24 2002

Extensions

Edited by Dean Hickerson, Jan 26 2002

a(8)-a(22) from Donovan Johnson, Jan 02 2009

Status

approved