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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. 5
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 (list; graph; refs; listen; history; text; internal format)
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: A193138 A255320 A256574 * A304820 A162641 A333487

Adjacent sequences:  A304816 A304817 A304818 * A304820 A304821 A304822

KEYWORD

sign

AUTHOR

Gus Wiseman, May 19 2018

STATUS

approved

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Last modified June 24 11:45 EDT 2021. Contains 345416 sequences. (Running on oeis4.)