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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.
2

%I #7 Jul 29 2018 10:44:09

%S 1,2,2,3,2,4,3,3,3,6,2,4,4,5,4,5,2,7,4,4,4,8,3,4,5,6,4,8,2,8,4,3,6,9,

%T 4,5,4,8,4,8,2,8,6,4,6,10,3,6,5,7,4,8,4,10,6,4,4,12,2,6,6,7,8,7,4,8,4,

%U 8,4,14,2,5,6,6,8,8,4,12,5,4,5,12,4,6,6,8,4,12,4,10,6,4,6,12,4,6,6,10,6,9

%N 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.

%e a(7)=3 because 1+U(7,x)=1+128x^7-192x^5+80x^3-8x=(2x+1)(8x^3-6x+1)(8x^3-4x^2-4x+1).

%o (PARI) p2 = 1; p1 = 2*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 02 2005

%Y Cf. A086327.

%Y Cf. A086374.

%K nonn,easy

%O 1,2

%A Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 06 2003

%E More terms from _David Wasserman_ and _Emeric Deutsch_, Mar 02 2005