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A300852
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L.g.f.: log(Product_{k>=1} (1 + x^prime(k))) = Sum_{n>=1} a(n)*x^n/n.
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3
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0, 2, 3, -2, 5, -1, 7, -2, 3, -3, 11, -5, 13, -5, 8, -2, 17, -1, 19, -7, 10, -9, 23, -5, 5, -11, 3, -9, 29, -6, 31, -2, 14, -15, 12, -5, 37, -17, 16, -7, 41, -8, 43, -13, 8, -21, 47, -5, 7, -3, 20, -15, 53, -1, 16, -9, 22, -27, 59, -10, 61, -29, 10, -2, 18, -12, 67, -19, 26, -10, 71, -5, 73, -35, 8
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OFFSET
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1,2
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} prime(k)*x^prime(k)/(1 + x^prime(k)).
a(n) = Sum_{p|n, p prime} p * (-1)^(n/p + 1). [See Mmca prog.]
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EXAMPLE
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L.g.f.: L(x) = 2*x^2/2 + 3*x^3/3 - 2*x^4/4 + 5*x^5/5 - x^6/6 + 7*x^7/7 - 2*x^8/8 + 3*x^9/9 - 3*x^10/10 + ...
exp(L(x)) = 1 + x^2 + x^3 + 2*x^5 + 2*x^7 + x^8 + x^9 + 2*x^10 + ... + A000586(n)*x^n + ...
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MATHEMATICA
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nmax = 75; Rest[CoefficientList[Series[Log[Product[(1 + x^Prime[k]), {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]]
nmax = 75; Rest[CoefficientList[Series[Sum[Prime[k] x^Prime[k]/(1 + x^Prime[k]), {k, 1, nmax}], {x, 0, nmax}], x]]
Table[DivisorSum[n, (-1)^(n/# + 1) # &, PrimeQ[#] &], {n, 75}]
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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