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A348608
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a(n) = Sum_{d|n, d <= sqrt(n)} (-1)^(d + n/d) * d.
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4
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1, -1, 1, 1, 1, -3, 1, 1, 4, -3, 1, -2, 1, -3, 4, 5, 1, -6, 1, -3, 4, -3, 1, 2, 6, -3, 4, -3, 1, -11, 1, 5, 4, -3, 6, 0, 1, -3, 4, 0, 1, -12, 1, -3, 9, -3, 1, 8, 8, -8, 4, -3, 1, -12, 6, -2, 4, -3, 1, -5, 1, -3, 11, 13, 6, -12, 1, -3, 4, -15, 1, 0, 1, -3, 9, -3, 8, -12, 1, 8
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OFFSET
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1,6
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} k * x^(k^2) / (1 + x^k).
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MATHEMATICA
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Table[DivisorSum[n, (-1)^(# + n/#) # &, # <= Sqrt[n] &], {n, 1, 80}]
nmax = 80; CoefficientList[Series[Sum[k x^(k^2)/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
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PROG
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(PARI) a(n) = sumdiv(n, d, if (d<=sqrt(n), (-1)^(d + n/d)*d)); \\ Michel Marcus, Oct 25 2021
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CROSSREFS
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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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