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A307423
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Dirichlet g.f.: zeta(2*s) / zeta(3*s).
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4
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1, 0, 0, 1, 0, 0, 0, -1, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1
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OFFSET
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1
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COMMENTS
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LINKS
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FORMULA
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Multiplicative with a(p) = 0, and a(p^e) = (-1)^e for e >= 2. - Amiram Eldar, Dec 25 2022
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MATHEMATICA
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Table[DivisorSum[n, Boole[Max[FactorInteger[#][[All, 2]]] < 3] * LiouvilleLambda[n/#]&], {n, 1, 100}]
f[p_, e_] := (-1)^e; f[p_, 1] := 0; 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^3)/(1-X^2))[n], ", ")) \\ Vaclav Kotesovec, Jun 14 2020
(PARI)
A212793(n) = factorback(apply(e->(e<=2), factor(n)[, 2]));
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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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EXTENSIONS
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STATUS
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approved
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