S000845


Numbers n such that the absolute value of the central term of cyclotomic(n,x) sets a new record.

0, 385, 4785, 7735, 11305, 17255, 20615, 26565, 40755, 106743, 327845, 886445, 983535, 1181895

1

S000845

The polynomial cyclotomic(n,x) is the n-degree cyclotomic polynomial. The record values of the central terms are in sequence S000846.

T. D. Noe, Plot of 14 terms

Andrew Arnold, A high-performance algorithm for calculating cyclotomic polynomials, 2010.

Andrew Arnold and Michael Monagan, Calculating cyclotomic polynomials, 2011.

(Mma) t = {{0,1}}; mx = 1; Do[If[Union[Transpose[FactorInteger[n]][[2]]] == {1}, c = CoefficientList[Cyclotomic[n, x], x]; q = c[[1 + EulerPhi[n]/2]]; If[Abs[q] > mx, mx = Abs[q]; AppendTo[t, {n, q}]]], {n, 3, 40755, 2}]; Transpose[t][[1]]

Cf. S000846.

nonn,hard

T. D. Noe, Feb 08 2016

© Tony D Noe 2014-2016