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%I #23 Feb 26 2024 10:09:43
%S -2,-3,-1,3,5,11,7,43,17,57,31,683,13,2731,127,331,257,43691,73,
%T 174763,205,5419,2047,2796203,241,1016801,8191,261633,3277,178956971,
%U 151,715827883,65537,1397419,131071,24214051
%N Cyclotomic polynomials at x=-2.
%C a(0) depends on the definition of the 0th cyclotomic polynomial; Maple defines it as x, but Mathematica defines it as 1. - _T. D. Noe_, Jul 23 2008 [a(0) = x is correct. - _N. J. A. Sloane_, Aug 01 2008]
%C A020501[2n] = A019320[n] for all odd n > 1. (Because if m > 1 is odd, then Phi_2m(x) = Phi_m(-x) as demonstrated by Bloom). - _Antti Karttunen_, Aug 02 2001
%H T. D. Noe, <a href="/A020501/b020501.txt">Table of n, a(n) for n = 0..1000</a>
%H D. M. Bloom, <a href="http://www.jstor.org/stable/2313417">On the Coefficients of the Cyclotomic Polynomials</a>, Amer.Math.Monthly 75, 372-377, 1968.
%H <a href="/index/Cy#CyclotomicPolynomialsValuesAtX">Index entries for cyclotomic polynomials, values at X</a>
%p with(numtheory,cyclotomic); f := n->subs(x=-2,cyclotomic(n,x)); seq(f(i),i=0..64);
%t Join[{-2}, Cyclotomic[Range[50], -2]] (* _Paolo Xausa_, Feb 26 2024 *)
%o (PARI) a(n) = if (n, polcyclo(n, -2), -2); \\ _Michel Marcus_, Mar 05 2016
%Y Cf. A020500, A020513.
%Y Cf. A105603
%K sign
%O 0,1
%A _Simon Plouffe_
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