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A020501
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Cyclotomic polynomials at x=-2.
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6
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-2, -3, -1, 3, 5, 11, 7, 43, 17, 57, 31, 683, 13, 2731, 127, 331, 257, 43691, 73, 174763, 205, 5419, 2047, 2796203, 241, 1016801, 8191, 261633, 3277, 178956971, 151, 715827883, 65537, 1397419, 131071, 24214051
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OFFSET
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0,1
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COMMENTS
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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]
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
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LINKS
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MAPLE
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with(numtheory, cyclotomic); f := n->subs(x=-2, cyclotomic(n, x)); seq(f(i), i=0..64);
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MATHEMATICA
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Join[{-2}, Cyclotomic[Range[50], -2]] (* Paolo Xausa, Feb 26 2024 *)
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PROG
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(PARI) a(n) = if (n, polcyclo(n, -2), -2); \\ Michel Marcus, Mar 05 2016
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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