A085122 a(n) = PrimePi(sigma(n)-phi(n)) - (PrimePi(sigma(n)) - PrimePi(phi(n))), where PrimePi = A000720, sigma = A000203 and phi = A000010.

0, -1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 2, 0, 1, 1, 2, 0, 2, 0, 2, 2, 2, 0, 2, 2, 2, 3, 3, 0, 2, 0, 3, 2, 2, 3, 3, 0, 3, 4, 3, 0, 4, 0, 3, 4, 3, 0, 4, 3, 5, 3, 5, 0, 3, 3, 3, 3, 3, 0, 3, 0, 4, 3, 4, 3, 4, 0, 5, 5, 5, 0, 4, 0, 2, 5, 4, 4, 4, 0, 5, 5, 5, 0, 7, 4, 5, 4, 5, 0, 4, 3, 5, 5, 5, 5, 4, 0, 5, 5, 5, 0, 6, 0, 6, 6, 7, 0, 5, 0, 5, 6, 8, 0, 5, 5, 6, 7, 5, 5, 5, 6, 5, 6, 7, 5, 5, 0, 7

Offset: 1

Author

Labos Elemer, Jul 11 2003

Keywords

• sign
• look

Comments

Scatterplot of this sequence shows interesting strata. - Antti Karttunen, Jan 22 2020

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A000010, A000203, A000720, A051612, A070803, A070804, A085343.

Programs

Mathematica

t=Table[PrimePi[DivisorSigma[1, w]-EulerPhi[w]]- (PrimePi[DivisorSigma[1, w]]-PrimePi[EulerPhi[w]]), {w, 1, 10000}]

PARI

A085122(n) = (primepi(sigma(n)-eulerphi(n)) - (primepi(sigma(n))-primepi(eulerphi(n)))); \\ Antti Karttunen, Jan 22 2020

Formula

a(n) = A000720(A051612(n)) - (A070803(n) - A070804(n)) = A000720(A051612(n)) - A085343(n). - Antti Karttunen, Jan 22 2020

Extensions

Name edited by Antti Karttunen, Jan 22 2020