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A320858
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a(n) = A320857(prime(n)).
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15
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0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 2, 3, 2, 1, 2, 3, 2, 3, 2, 3, 2, 3, 2, 1, 0, 1, 2, 1, 2, 1, 2, 1, 0, -1, 0, 1, 2, 1, 2, 3, 2, 3, 4, 3, 4, 5, 4, 5, 4, 5, 4, 5, 4, 3, 2, 3, 4, 5, 6, 5, 4, 5, 4, 5, 4, 5, 4, 3, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 6, 5, 4, 5, 6, 5, 6, 5, 4
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OFFSET
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1,11
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COMMENTS
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Among the first 10000 terms there are only 100 negative ones. See the comments about "Chebyshev's bias" in A320857.
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LINKS
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FORMULA
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a(n) = -Sum_{i=1..n} Kronecker(prime(i),2) = -Sum_{primes p<=n} Kronecker(2,prime(i)) = -Sum_{i=1..n} A091337(prime(i)).
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EXAMPLE
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prime(46) = 199, Pi(8,1)(199) = 8, Pi(8,5)(199) = 13, Pi(8,3)(199) = Pi(8,7)(199) = 12, so a(46) = 13 + 12 - 8 - 12 = 5.
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MATHEMATICA
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a[n_] := -Sum[KroneckerSymbol[-2, Prime[i]], {i, 1, n}];
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PROG
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(PARI) a(n) = -sum(i=1, n, kronecker(-2, prime(i)))
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CROSSREFS
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Let d be a fundamental discriminant.
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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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