A086327 Number of factors over Q in the factorization of the Chebyshev polynomial of the second kind U_n(x).

1, 2, 2, 2, 4, 2, 3, 4, 4, 2, 6, 2, 4, 6, 4, 2, 7, 2, 6, 6, 4, 2, 8, 4, 4, 6, 6, 2, 10, 2, 5, 6, 4, 6, 10, 2, 4, 6, 8, 2, 10, 2, 6, 10, 4, 2, 10, 4, 7, 6, 6, 2, 10, 6, 8, 6, 4, 2, 14, 2, 4, 10, 6, 6, 10, 2, 6, 6, 10, 2, 13, 2, 4, 10, 6, 6, 10, 2, 10, 8, 4, 2, 14, 6, 4, 6, 8, 2, 16, 6, 6, 6, 4, 6, 12, 2, 7, 10, 10, 2, 10, 2, 8, 14, 4

Offset

1,2

Comments

Initial terms are consistent with A069930(n+1). - Andrew Howroyd, Jul 10 2018

a(n) = A069930(n+1) at least for the first 1515 terms. - Antti Karttunen, Sep 25 2018

Links

Antti Karttunen, Table of n, a(n) for n = 1..1515

Gerzson Kéri, The factorization of compressed Chebyshev polynomials and other polynomials related to multiple-angle formulas, Annales Univ. Sci. Budapest (Hungary, 2022) Sect. Comp., Vol. 53, 93-108.

Prog

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

Crossrefs

Cf. A001227 (number of factors of Chebyshev polynomials of 1st kind).

Cf. A069930, A086375, A086389.

Sequence in context: A239452 A368468 A069930 * A114896 A216620 A181019

Adjacent sequences: A086324 A086325 A086326 * A086328 A086329 A086330

Keyword

nonn

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 30 2003

Extensions

a(11) corrected and a(19)-a(85) from Andrew Howroyd, Jul 10 2018

Terms a(86)-a(105) from Antti Karttunen, Sep 25 2018

Status

approved