A325699 Number of distinct even prime indices of n minus the number of distinct odd prime indices of n.

0, -1, 1, -1, -1, 0, 1, -1, 1, -2, -1, 0, 1, 0, 0, -1, -1, 0, 1, -2, 2, -2, -1, 0, -1, 0, 1, 0, 1, -1, -1, -1, 0, -2, 0, 0, 1, 0, 2, -2, -1, 1, 1, -2, 0, -2, -1, 0, 1, -2, 0, 0, 1, 0, -2, 0, 2, 0, -1, -1, 1, -2, 2, -1, 0, -1, -1, -2, 0, -1, 1, 0, -1, 0, 0, 0

Offset

1,10

Comments

A prime index of n is a number m such that prime(m) divides n. The multiset of prime indices of n is row n of A112798.

Links

Table of n, a(n) for n=1..76.

Formula

G.f.: Sum_{k>=1} (-1)^k * x^prime(k) / (1 - x^prime(k)). - Ilya Gutkovskiy, Feb 12 2020

Additive with a(p^e) = (-1)^primepi(p). - Amiram Eldar, Jun 17 2024

Mathematica

Table[Total[(-1)^PrimePi/@First/@If[n==1, {}, FactorInteger[n]]], {n, 100}]

Crossrefs

a(n) = A324967(n) - A324966(n).

Cf. A000712, A001221, A026010, A045931, A063886, A112798, A130780, A171966, A241638, A325698, A325700.

Sequence in context: A321930 A134023 A257931 * A293513 A015738 A333815

Adjacent sequences: A325696 A325697 A325698 * A325700 A325701 A325702

Keyword

sign

Author

Gus Wiseman, May 17 2019

Status

approved