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A154282
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Dirichlet inverse of A154281.
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4
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1, 0, 0, -1, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0
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OFFSET
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1,1
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COMMENTS
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Sequence is positive as often as negative.
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LINKS
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FORMULA
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Multiplicative with a(2^e) = (-1)^(e/2) if e is even and 0 is e is odd, and a(p^e) = 0 if p is an odd prime. - Amiram Eldar, Aug 27 2023
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MATHEMATICA
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nn = 95; a = PadRight[{1, 0, 0, 1}, nn, 0]; Inverse[Table[Table[If[Mod[n, k] == 0, a[[n/k]], 0], {k, 1, nn}], {n, 1, nn}]][[All, 1]] (* Mats Granvik, Jul 23 2017 *)
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PROG
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(PARI) a(n) = {my(e=valuation(n, 2)); if(e%2 == 0 && n == 1<<e, (-1)^(e/2), 0)} \\ Andrew Howroyd, Aug 05 2018
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CROSSREFS
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KEYWORD
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sign,easy,mult
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AUTHOR
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STATUS
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approved
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