A304819 Dirichlet convolution of r with zeta, where r(n) = (-1)^Omega(n) if n is 1 or not a perfect power and r(n) = 0 otherwise.

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

Offset

1,36

Comments

Omega(n) = A001222(n) is the number of prime factors of n counted with multiplicity.

Links

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

Formula

a(n) = Sum_{d|n, d = 1 or not a perfect power} (-1)^Omega(d).

Mathematica

Table[Sum[(-1)^PrimeOmega[d], {d, Select[Divisors[n], GCD@@FactorInteger[#][[All, 2]]==1&]}], {n, 100}]

Prog

(PARI) A304819(n) = sumdiv(n, d, if(!ispower(d), (-1)^bigomega(d), 0)); \\ Antti Karttunen, Jul 29 2018

Crossrefs

Positions of nonzero entries appear to be A126706.

Cf. A000005, A000007, A001222, A001597, A005117, A007916, A008683, A008836, A304362, A304653, A304779, A304817, A304820.

Sequence in context: A255320 A256574 A369427 * A304820 A382423 A162641

Adjacent sequences: A304816 A304817 A304818 * A304820 A304821 A304822

Keyword

sign

Author

Gus Wiseman, May 19 2018

Status

approved