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 A307427 Dirichlet g.f.: zeta(3*s) / (zeta(s) * zeta(2*s)). 1
 1, -1, -1, -1, -1, 1, -1, 2, -1, 1, -1, 1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, -2, -1, 1, 2, 1, -1, -1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -2, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -2, 1, -2, 1, 1, -1, -1, -1, 1, 1, 2, 1, -1, -1, 1, 1, -1, -1, -2, -1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Dirichlet convolution of A210826 and A271102. Dirichlet convolution of A307424 and A008683. LINKS Vaclav Kotesovec, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Dirichlet Generating Function Wikipedia, Dirichlet series MATHEMATICA nmax = 100; A271102 = Table[DivisorSum[n, Abs[MoebiusMu[#]] * MoebiusMu[n/#] &], {n, 1, nmax}]; Table[DivisorSum[n, Mod[DivisorSigma[0, n/#], 3, -1] * A271102[[#]] &], {n, 1, nmax}] nmax = 100; A307424 = Table[DivisorSum[n, Abs[MoebiusMu[#]] * Mod[DivisorSigma[0, n/#], 3, -1]&], {n, 1, nmax}]; Table[DivisorSum[n, MoebiusMu[#] * A307424[[n/#]] &], {n, 1, nmax}] PROG (PARI) for(n=1, 100, print1(direuler(p=2, n, (1-X)*(1-X^2)/(1-X^3))[n], ", ")) \\ Vaclav Kotesovec, Jun 14 2020 CROSSREFS Cf. A008683, A010057, A210826, A271102, A307424. Sequence in context: A063775 A053164 A295658 * A318672 A325989 A055229 Adjacent sequences:  A307424 A307425 A307426 * A307428 A307429 A307430 KEYWORD sign,mult AUTHOR Vaclav Kotesovec, Apr 08 2019 STATUS approved

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Last modified January 16 22:45 EST 2021. Contains 340213 sequences. (Running on oeis4.)