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A118205
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Euler transform of the negative of the Liouville function.
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5
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1, -1, 1, 0, -1, 2, -2, 2, 0, -2, 3, -2, 1, 2, -3, 3, -2, 0, 3, -2, 3, -2, 0, 2, -2, 3, -1, 0, 1, -2, 5, 0, 0, 1, -2, 1, 1, 2, 0, 1, -2, 1, 4, -1, 4, -2, -3, 6, -2, 5, 6, -8, 6, -4, 2, 9, -8, 7, -4, -1, 11, -1, 5, 1, -8, 5, 2, 4, 7, -8, 4, 2, 1, 14, -2, 0, -1, -6, 19, 2, 5, 6, -15, 12, 1, 3, 18, -17, 1, 9, 0, 29, -4, -3, 4, -13, 14, 17, 2, 0, -4
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OFFSET
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0,6
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LINKS
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Table of n, a(n) for n=0..100.
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FORMULA
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G.f.: A(x) = Product_{k>=1}(1 - x^k)^lambda(k) where lambda(k) is the Liouville function, A008836.
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MATHEMATICA
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nmax = 100; lambda[k_Integer?Positive] := If[ k > 1, (-1)^Total[ Part[Transpose[FactorInteger[k]], 2] ], 1 ]; CoefficientList[ Series[ Product[ (1 - x^k)^lambda[k], {k, 1, nmax} ], {x, 0, nmax} ], x ]
(* Second program (needs Mma >= 7.0): *)
nmax = 100;
Product[(1 - x^n)^LiouvilleLambda[n], {n, 1, nmax}] + O[x]^(nmax+1) // CoefficientList[#, x]& (* Jean-François Alcover, Jan 08 2020 *)
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CROSSREFS
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Cf. A061020, A117208, A118206, A118207, A118208.
Sequence in context: A118664 A223175 A322213 * A216265 A336694 A130277
Adjacent sequences: A118202 A118203 A118204 * A118206 A118207 A118208
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KEYWORD
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sign,easy
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AUTHOR
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Stuart Clary, Apr 15 2006
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STATUS
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approved
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