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A106475
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An alternating sum of greatest common divisors.
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5
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1, 0, 1, -4, 1, -8, 1, -16, -3, -16, 1, -36, 1, -24, -15, -48, 1, -48, 1, -68, -23, -40, 1, -112, -15, -48, -27, -100, 1, -120, 1, -128, -39, -64, -47, -180, 1, -72, -47, -208, 1, -176, 1, -164, -99, -88, 1, -304, -35, -160, -63, -196, 1, -216, -79, -304, -71, -112, 1, -420, 1, -120, -147, -320, -95, -288, 1, -260, -87
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OFFSET
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0,4
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COMMENTS
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With interpolated 0's, this is Sum_{k=0..n} gcd(n-k+1,k+1)*(-1)^k.
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LINKS
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FORMULA
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a(n) = Sum_{k=0..2*n} gcd(2*n-k+1, k+1)*(-1)^k.
Sum_{k=1..n} a(k) ~ n^2 * (1 - (4/Pi^2)*(log(n) + 2*gamma - 1/2 - log(2)/3 - zeta'(2)/zeta(2))), 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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easy,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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