A118208 G.f.: A(x) = Product_{k>=1} (1 + x^k)^(-lambda(k)) where lambda(k) is the Liouville function, A008836.

1, -1, 2, -1, 0, 2, -4, 5, -3, 0, 4, -6, 6, -2, -3, 8, -10, 6, 0, -6, 14, -13, 9, 0, -12, 17, -18, 11, 3, -18, 28, -22, 14, 7, -25, 30, -31, 11, 12, -23, 34, -28, 9, 12, -30, 35, -31, 10, 11, -30, 56, -35, 26, -4, -41, 51, -65, 48, -8, -28, 65, -74, 70, -9, -49, 71, -112, 69, -4, -48, 135, -129, 82, -21, -83, 155, -176, 99, 0

Offset

0,3

Links

Table of n, a(n) for n=0..78.

Wikipedia, Cyclotomic polynomial

Wikipedia, Liouville function

Formula

G.f.: A(x) = Product_{k >= 1} C(k,x^k)*C(2*k,x^(2*k)), where C(k,x) denotes the k-th cyclotomic polynomial. - Peter Bala, Mar 31 2023

Mathematica

nmax = 80; 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 ]

Crossrefs

Cf. A118205, A118206, A118207, A118209, A117211.

Sequence in context: A261615 A146162 A147702 * A355650 A292892 A074142

Adjacent sequences: A118205 A118206 A118207 * A118209 A118210 A118211

Keyword

sign,easy

Author

Stuart Clary, Apr 15 2006

Status

approved