A126271 a(n) = order of Galois group of the polynomial P(x) + n if P(x) + n (after dividing by the gcd of its coefficients) is irreducible, otherwise a(n) = 0, where P(x) = 128*x^8 - 256*x^6 + 160*x^4 - 32*x^2 + 1.

32, 32, 16, 32, 32, 32, 32, 32, 32, 16, 32, 32, 32, 16, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 32, 16, 16, 32, 32, 32

Offset: 0

Author

Artur Jasinski, Dec 23 2006

Keywords

• nonn

Comments

P(x) = T_8(x) is the degree 8 Chebyshev polynomial of the first kind.

Links

• Eric Weisstein's World of Mathematics, Chebyshev Polynomial of the First Kind

Crossrefs

Cf. A124827, A126270.

Programs

Magma

Q:=RationalField(); R:=PolynomialRing(Q); f:=128*x^8 - 256*x^6 + 160*x^4 - 32*x^2 + 0; for n in {0 .. 30} do f:=f+1; Order(GaloisGroup(f)); end for; /* N. J. A. Sloane */

Extensions

Edited by N. J. A. Sloane, Dec 28 2007