A086327 - OEIS

%I #14 Dec 20 2022 01:40:37

%S 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,

%T 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,

%U 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

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

%C Initial terms are consistent with A069930(n+1). - _Andrew Howroyd_, Jul 10 2018

%C a(n) = A069930(n+1) at least for the first 1515 terms. - _Antti Karttunen_, Sep 25 2018

%H Antti Karttunen, <a href="/A086327/b086327.txt">Table of n, a(n) for n = 1..1515</a>

%H Gerzson Kéri, <a href="http://ac.inf.elte.hu/Vol_053_2022/093_53.pdf">The factorization of compressed Chebyshev polynomials and other polynomials related to multiple-angle formulas</a>, Annales Univ. Sci. Budapest (Hungary, 2022) Sect. Comp., Vol. 53, 93-108.

%o (PARI) a(n)={vecsum(factor(polchebyshev(n, 2, x))[, 2])} \\ _Andrew Howroyd_, Jul 10 2018

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

%Y Cf. A069930, A086375, A086389.

%K nonn

%O 1,2

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

%E a(11) corrected and a(19)-a(85) from _Andrew Howroyd_, Jul 10 2018

%E Terms a(86)-a(105) from _Antti Karttunen_, Sep 25 2018