|
%I #15 Sep 02 2023 17:54:37
%S 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,
%T -18,11,3,-18,28,-22,14,7,-25,30,-31,11,12,-23,34,-28,9,12,-30,35,-31,
%U 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
%N G.f.: A(x) = Product_{k>=1} (1 + x^k)^(-lambda(k)) where lambda(k) is the Liouville function, A008836.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Cyclotomic_polynomial">Cyclotomic polynomial</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Liouville_function">Liouville function</a>
%F 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
%t 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 ]
%Y Cf. A118205, A118206, A118207, A118209, A117211.
%K sign,easy
%O 0,3
%A _Stuart Clary_, Apr 15 2006
|
