A086369 Number of factors over Q in the factorization of T_n(x) - 1 where T_n(x) is the Chebyshev polynomial of the first kind.

1, 2, 3, 4, 3, 6, 3, 6, 5, 6, 3, 10, 3, 6, 7, 8, 3, 10, 3, 10, 7, 6, 3, 14, 5, 6, 7, 10, 3, 14, 3, 10, 7, 6, 7, 16, 3, 6, 7, 14, 3, 14, 3, 10, 11, 6, 3, 18, 5, 10, 7, 10, 3, 14, 7, 14, 7, 6, 3, 22, 3, 6, 11, 12, 7, 14, 3, 10, 7, 14, 3, 22, 3, 6, 11, 10, 7, 14, 3, 18

Offset

1,2

Comments

If p is an odd prime then a(p) = 3.

Links

Antti Karttunen, Table of n, a(n) for n = 1..2049

Y. Z. Gurtas, Chebyshev polynomials and the minimal polynomial of cos(2pi/n), Am. Math. Monthly 124 (1) (2017) 73-78, Theorem 1.

Formula

a(n) = 1+2*A023645(n) for n odd, = 2+2*A023645(n) for n even. [Gurtas] - R. J. Mathar, Mar 03 2023

Prog

(PARI) a(n)={vecsum(factor(polchebyshev(n, 1, x)-1)[, 2])} \\ Andrew Howroyd, Jul 10 2018

Crossrefs

Cf. A086374.

Sequence in context: A290139 A317588 A080383 * A337532 A092089 A117659

Adjacent sequences: A086366 A086367 A086368 * A086370 A086371 A086372

Keyword

nonn

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 08 2003

Extensions

a(14) corrected and a(21)-a(80) added by Andrew Howroyd, Jul 10 2018

Status

approved