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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.

%I A126271 #7 Feb 16 2025 08:33:04
%S A126271 32,32,16,32,32,32,32,32,32,16,32,32,32,16,32,32,32,32,32,32,32,32,32,
%T A126271 32,32,32,16,16,32,32,32
%N 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.
%C A126271 P(x) = T_8(x) is the degree 8 Chebyshev polynomial of the first kind.
%H A126271 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ChebyshevPolynomialoftheFirstKind.html">Chebyshev Polynomial of the First Kind</a>
%o A126271 (Magma) Q:=RationalField(); R<x>:=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_ */
%Y A126271 Cf. A124827, A126270.
%K A126271 nonn
%O A126271 0,1
%A A126271 _Artur Jasinski_, Dec 23 2006
%E A126271 Edited by _N. J. A. Sloane_, Dec 28 2007