A158210 a(n) = omega(n) * (-1)^mu(n), where mu is the Moebius function.

0, -1, -1, 1, -1, -2, -1, 1, 1, -2, -1, 2, -1, -2, -2, 1, -1, 2, -1, 2, -2, -2, -1, 2, 1, -2, 1, 2, -1, -3, -1, 1, -2, -2, -2, 2, -1, -2, -2, 2, -1, -3, -1, 2, 2, -2, -1, 2, 1, 2, -2, 2, -1, 2, -2, 2, -2, -2, -1, 3, -1, -2, 2, 1, -2, -3, -1, 2, -2, -3, -1, 2, -1, -2, 2, 2, -2, -3, -1, 2, 1

Offset

1,6

Comments

Number n such that: a(n) < -1: A120944; a(n) = -1: A000040, a(n) > -1: A162966; a(n) = +1: A246547; a(n) > +1: A126706.

Links

Daniel Forgues, Table of n, a(n) for n = 1..10000

Formula

a(n) = omega(n) * (-1)^mu(n), where mu is the Moebius function.

a(n) = A001221(n) * (-1)^A008683(n).

a(mn) = [|a(m)| + |a(n)|] * max(sign[a(n)], sign[a(m)]), gcd(m,n) = 1, m > 1, n > 1.

Mathematica

Table[(-1)^MoebiusMu[n]*PrimeNu[n], {n, 81}] (* L. Edson Jeffery, Dec 08 2014 *)

Crossrefs

Cf. A001221 (omega), A008683 (mu).

Cf. A120944, A000040, A162966, A246547, A126706.

Sequence in context: A237353 A293460 A231813 * A322307 A087802 A079553

Adjacent sequences: A158207 A158208 A158209 * A158211 A158212 A158213

Keyword

sign

Author

Daniel Forgues, Mar 14 2009

Extensions

Edited by Joerg Arndt, Feb 12 2024

Status

approved