A086783 Discriminant of the polynomial x^n - 1.

1, 4, -27, -256, 3125, 46656, -823543, -16777216, 387420489, 10000000000, -285311670611, -8916100448256, 302875106592253, 11112006825558016, -437893890380859375, -18446744073709551616, 827240261886336764177, 39346408075296537575424, -1978419655660313589123979

Offset: 1

Author

Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 03 2003

Keywords

• sign
• easy

Comments

By definition, a(n) = Product_{1<=iJianing Song, Mar 17 2021

Links

• Kenneth G. Hawes, Table of n, a(n) for n = 1..386
• Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 249-255. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012.

Crossrefs

Cf. A000312, A004124.

Programs

PARI

a(n)=poldisc('x^n-1); \\ Joerg Arndt, May 04 2013

Sage

def A086783(n) : return (-1)^((n-1)//2) * n^n # Eric M. Schmidt, May 04 2013

Formula

a(n) = (-1)^floor((n-1)/2) * n^n = (-1)^floor((n-1)/2) * A000312(n).

Extensions

More terms from Eric M. Schmidt, May 04 2013