A066850 Numbers n such that phi(phi(n)) + sigma(sigma(n)) = phi(sigma(n)) + sigma(phi(n)), where phi=A000010 is Euler's totient function and sigma=A000203 is the sum of divisors function.

1, 4, 2669, 9559, 15293, 32583, 36593, 38443, 255367, 257239, 273977, 283391, 314101, 421553, 488363, 532975, 768699, 839973, 871757, 1960479, 2337221, 2374867, 3084659, 3326653, 3735029, 4440017, 5387373, 7930439, 8114377

Offset

1,2

Links

Harry J. Smith, Table of n, a(n) for n = 1..114

Example

Let n = 2669. Then phi(phi(n)) + sigma(sigma(n)) = phi(2496) + sigma(2844) = 768 + 7280 = 8048 and phi(sigma(n)) + sigma(phi(n)) = phi(2844) + sigma(2496) = 936 + 7112 = 8048. So 2669 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]; c + d - e - f]; Do[If[g[n] == 0, Print[n]], {n, 1, 10^6}]

Prog

(PARI) { n=0; for (m=1, 10^10, e=eulerphi(m); s=sigma(m); if (eulerphi(e) + sigma(s) == eulerphi(s) + sigma(e), write("b066850.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Apr 02 2010

Crossrefs

Sequence in context: A280790 A079187 A131587 * A066837 A275683 A297008

Adjacent sequences: A066847 A066848 A066849 * A066851 A066852 A066853

Keyword

nonn

Author

Joseph L. Pe, Jan 24 2002

Extensions

Edited by Dean Hickerson, Jan 24 2002

Status

approved