cp's OEIS Frontend

A137979 Highest coefficient occurring in the factorization of x^n - 1 over the reals.

%I A137979 #16 Jul 22 2020 11:39:23
%S A137979 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%T A137979 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A137979 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2
%N A137979 Highest coefficient occurring in the factorization of x^n - 1 over the reals.
%C A137979 Based on a comment in Mathematica helpfile ref/Factor - Neat Examples.
%C A137979 The first factorization of x^n - 1 in which a 2 appears as a coefficient is for n=105.
%C A137979 Different from A160338, see comment there.
%H A137979 N. J. A. Sloane, <a href="/A137979/b137979.txt">Table of n, a(n) for n = 1..10000</a>
%e A137979 a(4) = 1 because x^4 - 1 = (x^2+1)(x+1)(x-1) and the highest coefficient of these three terms is 1.
%e A137979 The first time a 2 appears is at n=105, where the factorization is:
%e A137979 (x-1)*(x^6+x^5+x^4+x^3+x^2+x+1)*(x^4+x^3+x^2+x+1)*
%e A137979 (x^24-x^23+x^19-x^18+x^17-x^16+x^14-x^13+x^12-x^11+x^10-x^8+x^7-x^6+x^5-x+1)*
%e A137979 (x^2+x+1)*(x^12-x^11+x^9-x^8+x^6-x^4+x^3-x+1)*
%e A137979 (x^8-x^7+x^5-x^4+x^3-x+1)*
%e A137979 (x^48+x^47+x^46-x^43-x^42-2*x^41-x^40-x^39+x^36+x^35+x^34+x^33+x^32+x^31-x^28-x^26-x^24-x^22-x^20+x^17+x^16+x^15+x^14+x^13+x^12-x^9-x^8-2*x^7-x^6-x^5+x^2+x+1). - _N. J. A. Sloane_, Apr 18 2008
%t A137979 Table[Max[Abs[Flatten[CoefficientList[Transpose[FactorList[x^i - 1]][[1]], x]]]], {i, 1, 1000}]
%o A137979 (PARI) a(n) = {my(f = factor(x^n-1)); vecmax(vector(#f~, k, vecmax(apply(x->abs(x), Vec(f[k,1])))));} \\ _Michel Marcus_, Dec 05 2018
%Y A137979 Cf. A013590, A013594.
%K A137979 nonn
%O A137979 1,105
%A A137979 _Ian Miller_, Feb 25 2008