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A344373
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a(n) = Sum_{k=1..n-1} (-1)^k gcd(k, n).
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5
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0, -1, 0, 0, 0, -1, 0, 4, 0, -1, 0, 8, 0, -1, 0, 16, 0, 3, 0, 16, 0, -1, 0, 36, 0, -1, 0, 24, 0, 15, 0, 48, 0, -1, 0, 48, 0, -1, 0, 68, 0, 23, 0, 40, 0, -1, 0, 112, 0, 15, 0, 48, 0, 27, 0, 100, 0, -1, 0, 120, 0, -1, 0, 128, 0, 39, 0, 64, 0, 47, 0, 180, 0, -1, 0, 72, 0, 47, 0, 208, 0, -1, 0, 176, 0, -1, 0, 164, 0, 99
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OFFSET
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1,8
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COMMENTS
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The usual OEIS policy is not to include sequences like this where alternate terms are zero; this is an exception.
For all n, a(n) >= -1. Equality holds for n = 2 and n = 2*p for an odd prime p.
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LINKS
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FORMULA
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a(2*n+1) = 0.
Sum_{k=1..n} a(k) ~ (n^2/4) * ((4/Pi^2)*(log(n) + 2*gamma - 1/2 - 4*log(2)/3 - zeta'(2)/zeta(2)) - 1), where gamma is Euler's constant (A001620). - Amiram Eldar, Mar 30 2024
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MATHEMATICA
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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