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A193056
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Reciprocals are the complement to logarithm of Riemann zeta. a(1)=0, for n>1: a(n) = A008683(n) + A100995(n).
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2
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0, 0, 0, 2, 0, 1, 0, 3, 2, 1, 0, 0, 0, 1, 1, 4, 0, 0, 0, 0, 1, 1, 0, 0, 2, 1, 3, 0, 0, -1, 0, 5, 1, 1, 1, 0, 0, 1, 1, 0, 0, -1, 0, 0, 0, 1, 0, 0, 2, 0, 1, 0, 0, 0, 1, 0, 1, 1, 0, 0, 0, 1, 0, 6, 1, -1, 0, 0, 1, -1, 0, 0, 0, 1, 0, 0, 1, -1, 0, 0, 4, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, -1, 0, 0, -1, 1, 0, 0, 0, -1, 1, 0, 0, -1, 1, 0, 0, 1, 1, 0
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OFFSET
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1,4
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COMMENTS
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The characteristic function of primes can be computed as: A010051(n) = A100995(n) - sqrt(A100995(n)*a(n)). But the element-wise multiplication of the sequences inside the sqrt, has no known operation or definition in terms of Dirichlet generating functions.
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LINKS
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FORMULA
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Dirichlet series generating function of reciprocals: -0/1*(Zeta(s)-1)^1 + 1/2*(Zeta(s)-1)^2 - 2/3*(Zeta(s)-1)^3 + 3/4*(Zeta(s)-1)^4 - ...
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EXAMPLE
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The reciprocals of this sequence, defined by the Dirichlet series generating function are: 0/1,0/1,0/1,1/2,0/1,1/1,0/1,1/3,1/2,1/1, 0/1,0/1...
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MATHEMATICA
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a100995[n_]:=If[PrimePowerQ[n], FactorInteger[n][[1, 2]], 0] (* From Harvey P. Dale *); Table[If[n==1, 0, MoebiusMu[n] + a100995[n]], {n, 100}] (* Indranil Ghosh, May 27 2017 *)
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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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EXTENSIONS
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STATUS
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approved
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