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A307427
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Dirichlet g.f.: zeta(3*s) / (zeta(s) * zeta(2*s)).
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1
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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
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OFFSET
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1,8
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COMMENTS
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LINKS
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FORMULA
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Multiplicative with a(p^e) = 2 if e == 0 (mod 3), and -1 otherwise. - Amiram Eldar, Dec 25 2022
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MATHEMATICA
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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}]
f[p_, e_] := If[Divisible[e, 3], 2, -1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Dec 25 2022 *)
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PROG
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(PARI) for(n=1, 100, print1(direuler(p=2, n, (1-X)*(1-X^2)/(1-X^3))[n], ", ")) \\ Vaclav Kotesovec, Jun 14 2020
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CROSSREFS
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KEYWORD
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sign,mult
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AUTHOR
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STATUS
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approved
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