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A325939
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Expansion of Sum_{k>=1} x^(2*k) / (1 + x^k).
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4
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0, 1, -1, 2, -1, 1, -1, 3, -2, 1, -1, 3, -1, 1, -3, 4, -1, 1, -1, 3, -3, 1, -1, 5, -2, 1, -3, 3, -1, 1, -1, 5, -3, 1, -3, 4, -1, 1, -3, 5, -1, 1, -1, 3, -5, 1, -1, 7, -2, 1, -3, 3, -1, 1, -3, 5, -3, 1, -1, 5, -1, 1, -5, 6, -3, 1, -1, 3, -3, 1, -1, 7, -1, 1, -5, 3, -3, 1, -1, 7
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OFFSET
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1,4
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COMMENTS
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Number of even divisors of n minus number of odd strong divisors of n (i.e. odd divisors > 1).
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LINKS
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FORMULA
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G.f.: Sum_{k>=2} (-1)^k * x^k / (1 - x^k).
a(n) = Sum_{d|n, d>1} (-1)^d.
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MATHEMATICA
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nmax = 80; CoefficientList[Series[Sum[x^(2 k)/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
Table[DivisorSum[n, (-1)^# &, # > 1 &], {n, 1, 80}]
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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