A086369 - OEIS

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

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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