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%I #10 Sep 23 2023 03:13:55
%S 1,2,3,2,3,4,3,2,5,4,3,4,3,4,7,2,3,6,3,4,7,4,3,4,5,4,7,4,3,8,3,2,7,4,
%T 7,6,3,4,7,4,3,8,3,4,11,4,3,4,5,6,7,4,3,8,7,4,7,4,3,8,3,4,11,2,7,8,3,
%U 4,7,8,3,6,3,4,11,4,7,8,3,4,9,4,3,8,7,4,7,4,3,12,7,4,7,4,7,4,3,6,11,6,3,8,3
%N 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.
%H Antti Karttunen, <a href="/A086374/b086374.txt">Table of n, a(n) for n = 1..2049</a>
%F If p is an odd prime then a(p) = 3.
%e a(6) = 4 because T_6(x)+1 = 32x^6-48x^4+18x^2 = x^2*(4x^2-3)^2.
%o (PARI) p2 = 1; p1 = x; for (n = 1, 103, p = 2*x*p1 - p2; f = factor(p1 + 1); print(sum(i = 1, matsize(f)[1], f[i, 2]), " "); p2 = p1; p1 = p); \\ _David Wasserman_, Mar 03 2005
%o (PARI) A086374(n) = {vecsum(factor(polchebyshev(n, 1, x)+1)[, 2])}; \\ _Antti Karttunen_, Sep 27 2018, after _Andrew Howroyd_'s program for A086369
%Y Cf. A001227, A086369.
%K nonn,easy
%O 1,2
%A Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 06 2003
%E More terms from _David Wasserman_, Mar 03 2005
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