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A317531
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Expansion of Sum_{p prime, k>=1} x^(p^k)/(1 + x^(p^k)).
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2
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0, 1, 1, 0, 1, 0, 1, -1, 2, 0, 1, -1, 1, 0, 2, -2, 1, -1, 1, -1, 2, 0, 1, -2, 2, 0, 3, -1, 1, -1, 1, -3, 2, 0, 2, -2, 1, 0, 2, -2, 1, -1, 1, -1, 3, 0, 1, -3, 2, -1, 2, -1, 1, -2, 2, -2, 2, 0, 1, -2, 1, 0, 3, -4, 2, -1, 1, -1, 2, -1, 1, -3, 1, 0, 3, -1, 2, -1, 1, -3, 4, 0, 1, -2, 2, 0, 2, -2, 1, -2, 2, -1, 2, 0, 2
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OFFSET
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1,9
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LINKS
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FORMULA
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L.g.f.: log(Product_{p prime, k>=1} (1 + x^(p^k))^(1/p^k)) = Sum_{n>=1} a(n)*x^n/n.
a(n) = Sum_{d|n} (-1)^(n/d+1)*A069513(d).
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MATHEMATICA
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nmax = 95; Rest[CoefficientList[Series[Sum[Boole[PrimePowerQ[k]] x^k/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x]]
nmax = 95; Rest[CoefficientList[Series[Log[Product[(1 + Boole[PrimePowerQ[k]] x^k)^(1/k), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]]
Table[DivisorSum[n, (-1)^(n/# + 1) &, PrimePowerQ[#] &], {n, 95}]
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PROG
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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