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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.

+0
4

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, 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, 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 (list; graph; listen)

	OFFSET	`1,2`
	FORMULA	`If p is an odd prime then a(p) = 3.`
	EXAMPLE	`a(6) = 4 because T_6(x)+1 = 32x^6-48x^4+18x^2 = x^2*(4x^2-3)^2.`
	PROGRAM	`(PARI) p2 = 1; p1 = x; for (n = 1, 103, p = 2xp1 - p2; f = factor(p1 + 1); print(sum(i = 1, matsize(f)[1], f[i, 2]), " "); p2 = p1; p1 = p); (Wasserman)`
	CROSSREFS	`Cf. A001227.` `Sequence in context: A106383 A105500 A088748 this_sequence A123182 A069464 A100795` `Adjacent sequences: A086371 A086372 A086373 this_sequence A086375 A086376 A086377`
	KEYWORD	`nonn,easy`
	AUTHOR	`Yuval Dekel (dekelyuval(AT)hotmail.com), Sep 06 2003`
	EXTENSIONS	`More terms from David Wasserman (wasserma(AT)spawar.navy.mil), Mar 03 2005`

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Last modified November 21 14:49 EST 2008. Contains 150807 sequences.

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