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A081295
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a(n) = (-1)^(n+1) * coefficient of x^n in Sum_{k>=1} x^k/(1+2*x^k).
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7
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1, 1, 5, 9, 17, 29, 65, 137, 261, 497, 1025, 2085, 4097, 8129, 16405, 32905, 65537, 130845, 262145, 524793, 1048645, 2096129, 4194305, 8390821, 16777233, 33550337, 67109125, 134225865, 268435457, 536855053, 1073741825, 2147516553, 4294968325, 8589869057
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = (-1)^(n+1) * [x^n]( Sum_{k>=1} x^k/(1+2*x^k) ).
a(p) = 2^(p-1) - 1, for p prime.
a(n) = (-1)^(n+1) * Sum_{d|n} (-2)^(d-1). - Robert Israel, Jun 04 2018
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MAPLE
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f:= n -> (-1)^(n+1)*add((-2)^(d-1), d=numtheory:-divisors(n)):
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MATHEMATICA
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A081295[n_]:= (-1)^(n+1)*DivisorSum[n, (-2)^(#-1) &];
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PROG
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(PARI) a(n) =if(n<1, 0, (-1)^(n+1)*polcoeff(sum(k=1, n, x^k/(1+2*x^k), x*O(x^n)), n))
(Magma)
A081295:= func< n | (-1)^(n+1)*(&+[(-2)^(d-1): d in Divisors(n)]) >;
(SageMath)
def A081295(n): return (-1)^(n+1)*sum((-2)^(k-1) for k in (1..n) if (k).divides(n))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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