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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. 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; refs; listen; history; text; internal format)
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); (Wasserman)

(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

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Last modified December 1 16:44 EST 2021. Contains 349430 sequences. (Running on oeis4.)