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A086375 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
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, 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, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..100.

EXAMPLE

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).

PROG

(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

CROSSREFS

Cf. A086327.

Cf. A086374.

Sequence in context: A337327 A065770 A297113 * A107324 A023522 A205000

Adjacent sequences:  A086372 A086373 A086374 * A086376 A086377 A086378

KEYWORD

nonn,easy

AUTHOR

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

EXTENSIONS

More terms from David Wasserman and Emeric Deutsch, Mar 02 2005

STATUS

approved

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Last modified December 5 03:52 EST 2021. Contains 349530 sequences. (Running on oeis4.)