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A299406
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Dirichlet g.f.: Sum_{n>0} a(n)/n^s = (zeta(s)*zeta(6*s))/(zeta(2*s)*zeta(3*s)).
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5
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1, 1, 1, 0, 1, 1, 1, -1, 0, 1, 1, 0, 1, 1, 1, -1, 1, 0, 1, 0, 1, 1, 1, -1, 0, 1, -1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, -1, 1, 1, 1, 0, 0, 1, 1, -1, 0, 0, 1, 0, 1, -1, 1, -1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, -1, -1, 1, 1, 0, 1, 1, 1, -1, 1, 0, 1, 0, 1, 1
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OFFSET
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1,1
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LINKS
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FORMULA
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a(n) is multiplicative with a(p^e)=(-1)^(e mod 3 + e mod 6) if e mod 3 < 2, otherwise 0, p prime and e >= 0.
Dirichlet inverse b(n) is multiplicative with b(p^e) = (-1)^e if e < 3, otherwise 0, p prime and e >= 0.
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MATHEMATICA
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f[e_] := If[Mod[e, 3] < 2, (-1)^(Mod[e, 3] + Mod[e, 6]), 0];
a[n_] := a[n] = Times @@ (f /@ FactorInteger[n][[All, 2]]);
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PROG
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(PARI) A299406(n) = { my(es = factor(n)[, 2]); factorback(apply(e -> if(2==(e%3), 0, (-1)^((e%3)+(e%6))), es)); }; \\ Antti Karttunen, Jul 29 2018
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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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