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A020513 Cyclotomic polynomials evaluated at x=-1. 8
-1, -2, 0, 1, 2, 1, 3, 1, 2, 1, 5, 1, 1, 1, 7, 1, 2, 1, 3, 1, 1, 1, 11, 1, 1, 1, 13, 1, 1, 1, 1, 1, 2, 1, 17, 1, 1, 1, 19, 1, 1, 1, 1, 1, 1, 1, 23, 1, 1, 1, 5, 1, 1, 1, 3, 1, 1, 1, 29, 1, 1, 1, 31, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Robert Israel, Table of n, a(n) for n = 0..10000

E. T. Bell, Cauchy’s cyclotomic function and functional powers, Bull. Amer. Math. Soc. 33 (1927), 416-422.

Bartlomiej Bzdega, Andres Herrera-Poyatos, Pieter Moree, Cyclotomic polynomials at roots of unity, arXiv:1611.06783 [math.NT], 2016. See Lemma 22.

FORMULA

For n >= 3: if n = 2*p^m with a prime p then a(n) = p otherwise a(n) = 1. - Ola Veshta (olaveshta(AT)my-deja.com), Jun 01 2001

MAPLE

with(numtheory, cyclotomic); f := n->subs(x=-1, cyclotomic(n, x)); seq(f(i), i=0..64);

MATHEMATICA

Array[Cyclotomic[#, -1] &, 90, 0] (* Robert G. Wilson v, Nov 23 2016 *)

PROG

(PARI) a(n) = if (n==0, -1, subst(polcyclo(n), x, -1)); \\ Michel Marcus, Apr 22 2016

(PARI) a(n) = if (n==0, -1, if (n==1, -2, if (n==2, 0, if (!(n % 2) && isprimepower(n/2, &p), p, 1)))); \\ Michel Marcus, Nov 23 2016

CROSSREFS

Cf. A138929 (2*p^m, m >= 0 values).

Sequence in context: A077905 A131331 A268696 * A029276 A109248 A131866

Adjacent sequences:  A020510 A020511 A020512 * A020514 A020515 A020516

KEYWORD

sign

AUTHOR

Simon Plouffe

STATUS

approved

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Last modified April 25 10:11 EDT 2017. Contains 285379 sequences.