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A348515
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a(n) = Sum_{d|n, d <= sqrt(n)} (-1)^(n/d + 1).
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3
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1, -1, 1, -2, 1, 0, 1, -2, 2, 0, 1, -3, 1, 0, 2, -3, 1, -1, 1, -1, 2, 0, 1, -4, 2, 0, 2, -1, 1, -2, 1, -3, 2, 0, 2, -3, 1, 0, 2, -4, 1, 0, 1, -1, 3, 0, 1, -5, 2, -1, 2, -1, 1, 0, 2, -4, 2, 0, 1, -4, 1, 0, 3, -4, 2, 0, 1, -1, 2, -2, 1, -4, 1, 0, 3, -1, 2, 0, 1, -5
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OFFSET
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1,4
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LINKS
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FORMULA
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G.f.: Sum_{k>=1} (-1)^(k + 1) * x^(k^2) / (1 + x^k).
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MATHEMATICA
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Table[DivisorSum[n, (-1)^(n/# + 1) &, # <= Sqrt[n] &], {n, 1, 80}]
nmax = 80; CoefficientList[Series[Sum[(-1)^(k + 1) x^(k^2)/(1 + x^k), {k, 1, nmax}], {x, 0, nmax}], x] // Rest
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PROG
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(Python)
from sympy import divisors
def a(n): return sum((-1)**(n//d + 1) for d in divisors(n) if d*d <= n)
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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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