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A118209
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G.f.: A(x) = sum_{k>=1} lambda(k) * k * x^k/(1 + x^k) where lambda(k) is the Liouville function, A008836.
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2
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1, -3, -2, 5, -4, 6, -6, -11, 7, 12, -10, -10, -12, 18, 8, 21, -16, -21, -18, -20, 12, 30, -22, 22, 21, 36, -20, -30, -28, -24, -30, -43, 20, 48, 24, 35, -36, 54, 24, 44, -40, -36, -42, -50, -28, 66, -46, -42, 43, -63, 32, -60, -52, 60, 40, 66, 36, 84, -58, 40, -60, 90, -42, 85, 48, -60, -66, -80, 44, -72, -70, -77, -72, 108, -42
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Related to the logarithmic derivative of A118207(x) and A118208(x).
Related to a signed variant of A022998 via Mobius inversion. - R. J. Mathar, Jul 03 2011
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FORMULA
| a(n) = sum_{d|n} (-1)^(n/d - 1) lambda(d) d, Dirichlet convolution of A061019 and A062157.
G.f.: A(x) is x times the logarithmic derivative of A118207(x).
G.f.: A(x) = A061020(x) - 2 A061020(x^2).
Dirichlet g.f.: zeta(s)*zeta(2s-2)*(1-2^(1-s))/zeta(s-1). - R. J. Mathar, Jul 03 2011
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MATHEMATICA
| nmax = 80; lambda[k_Integer?Positive] := If[ k > 1, (-1)^Total[ Part[Transpose[FactorInteger[k]], 2] ], 1 ]; Drop[ CoefficientList[ Series[ Sum[ lambda[k] k x^k/(1 + x^k), {k, 1, nmax} ], {x, 0, nmax} ], x ], 1 ]
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CROSSREFS
| Cf. A118207, A118208, A117212.
Sequence in context: A049820 A109712 A095049 * A109451 A160017 A193231
Adjacent sequences: A118206 A118207 A118208 * A118210 A118211 A118212
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KEYWORD
| sign,easy,mult
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AUTHOR
| Stuart Clary (clary(AT)uakron.edu), Apr 15, 2006
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