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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.

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`%I #9 Dec 20 2022 01:40:33
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`%S 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,
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`%T 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,
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`%U 8,4,9,2,12,6,4,8,8,4,8,5,10,5,6,4,12,6
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`%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.
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`%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.
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`%o (PARI) a(n)={vecsum(factor(polchebyshev(n,2,x)-1)[,2])} \\ _Andrew Howroyd_, Jul 10 2018
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`%Y Cf. A086375.
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`%K nonn
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`%O 1,3
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`%A Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 08 2003
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`%E a(21)-a(85) from _Andrew Howroyd_, Jul 10 2018
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