A066945 Numbers n such that phi(phi(n)) + sigma(sigma(n)) - phi(sigma(n)) - sigma(phi(n)) = phi(n).

11, 11063, 11943, 38585, 39995, 43021, 63349, 67709, 967393, 1267511, 2020925, 2915307, 5805559, 6584747, 6659429, 8064017, 26260385, 27681847, 31886881, 41932769, 48922307, 61270145, 71429011, 89087903, 91364345, 191945623

Offset

1,1

Links

Harry J. Smith, Table of n, a(n) for n = 1..39

Example

Let n = 11. Then phi(phi(n)) + sigma(sigma(n)) - phi(sigma(n)) - sigma(phi(n)) = phi(10) + sigma(12) - phi(12) - sigma(10) = 4 + 28 - 4 - 18 = 10 = phi(n), so 11 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==a]; Do[If[g[n]==True, Print[n]], {n, 1, 10^5}]

Prog

(PARI) { n=0; for (m=1, 10^10, e=eulerphi(m); s=sigma(m); if (eulerphi(e) + sigma(s) - eulerphi(s) - sigma(e) == e, write("b066945.txt", n++, " ", m); if (n==1000, return)) ) } \\ Harry J. Smith, Apr 11 2010

Crossrefs

Cf. A000010, A000203, A066850, A066939, A066946.

Sequence in context: A267923 A068223 A068224 * A267359 A267940 A113615

Adjacent sequences: A066942 A066943 A066944 * A066946 A066947 A066948

Keyword

nonn

Author

Joseph L. Pe, Jan 24 2002

Extensions

Edited by Dean Hickerson, Jan 26 2002

a(17)-a(26) from Donovan Johnson, Jan 02 2009

Status

approved