A086374 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.

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

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..2049

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.

Prog

(PARI) p2 = 1; p1 = 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 03 2005
(PARI) A086374(n) = {vecsum(factor(polchebyshev(n, 1, x)+1)[, 2])}; \\ Antti Karttunen, Sep 27 2018, after Andrew Howroyd's program for A086369

Crossrefs

Cf. A001227, A086369.

Sequence in context: A288569 A088748 A323235 * A322591 A332827 A325811

Adjacent sequences: A086371 A086372 A086373 * A086375 A086376 A086377

Keyword

nonn,easy

Author

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

Extensions

More terms from David Wasserman, Mar 03 2005

Status

approved