A086389 Number of factors over Q in the factorization of U_n(x) - 1 where U_n(x) is the Chebyshev polynomial of the second kind.

1, 1, 2, 3, 2, 3, 3, 4, 3, 4, 2, 6, 4, 3, 4, 6, 2, 6, 4, 6, 4, 4, 3, 8, 5, 4, 4, 8, 2, 7, 4, 6, 6, 5, 4, 9, 4, 4, 4, 10, 2, 8, 6, 6, 6, 4, 3, 11, 5, 6, 4, 8, 4, 8, 6, 8, 4, 6, 2, 12, 6, 3, 8, 9, 4, 8, 4, 8, 4, 9, 2, 12, 6, 4, 8, 8, 4, 8, 5, 10, 5, 6, 4, 12, 6

Offset: 1

Author

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

Keywords

• nonn

Links

• 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.

Crossrefs

Cf. A086375.

Programs

PARI

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

Extensions

a(21)-a(85) from Andrew Howroyd, Jul 10 2018