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A328705
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Dirichlet g.f.: Product_{k>=1} zeta(k*s)^2.
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1
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1, 2, 2, 5, 2, 4, 2, 10, 5, 4, 2, 10, 2, 4, 4, 20, 2, 10, 2, 10, 4, 4, 2, 20, 5, 4, 10, 10, 2, 8, 2, 36, 4, 4, 4, 25, 2, 4, 4, 20, 2, 8, 2, 10, 10, 4, 2, 40, 5, 10, 4, 10, 2, 20, 4, 20, 4, 4, 2, 20, 2, 4, 10, 65, 4, 8, 2, 10, 4, 8, 2, 50, 2, 4, 10, 10, 4, 8, 2, 40
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OFFSET
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1,2
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COMMENTS
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Dirichlet convolution of A000688 with itself.
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LINKS
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FORMULA
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Sum_{k=1..n} a(k) ~ c^2 * n * (log(n) + 2*gamma - 1 - 2*s), where c = A021002 = Product_{k>=2} zeta(k) = 2.2948565916733137941835158313443112887131637994..., s = Sum_{k>=2} k*zeta'(k)/zeta(k) = -2.1955691982567064617939038695473479681910375... and gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Oct 26 2019
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MATHEMATICA
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Table[DivisorSum[n, FiniteAbelianGroupCount[n/#] FiniteAbelianGroupCount[#] &], {n, 1, 80}]
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CROSSREFS
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KEYWORD
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nonn,mult
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AUTHOR
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STATUS
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approved
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