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.

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

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 A366311

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