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

1,3

Links

Table of n, a(n) for n=1..85.

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)-1)[, 2])} \\ Andrew Howroyd, Jul 10 2018

Crossrefs

Cf. A086375.

Sequence in context: A319982 A304331 A241834 * A128622 A026256 A079715

Adjacent sequences: A086386 A086387 A086388 * A086390 A086391 A086392

Keyword

nonn

Author

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

Extensions

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

Status

approved