A203411 Discriminant of the cyclotomic binomial period polynomial for an odd prime.

1, 5, 49, 14641, 371293, 410338673, 16983563041, 41426511213649, 10260628712958602189, 756943935220796320321, 456487940826035155404146917, 4394336169668803158610484050361, 467056167777397914441056671494001, 6111571184724799803076702357055363809

Offset: 2

Author

Franz Vrabec, Jan 01 2012

Keywords

• nonn

Examples

			a(5) = 11^4 = 14641, because prime(5) = 11.
		

Links

• 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. 251-257. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012.
• J. Brillhart, Note on the discriminant of certain cyclotomic period polynomials, Pacific Journal of Mathematics, 152/1(1992), 15-19.
• L. Carlitz and F. R. Olson, Maillet's determinant, Proceedings of the American Mathematical Society, 6/2 (1955), 265-269.
• L. Carlitz, A special determinant, Proceedings of the American Mathematical Society, 6/2 (1955), 270-272.

Crossrefs

Cf. A152291.

Programs

Mathematica

#^((#-3)/2)&/@Prime[Range[2,20]] (* Harvey P. Dale, Aug 11 2023 *)

PARI

a(n) = prime(n)^((prime(n)-3)/2); \\ Michel Marcus, Apr 15 2017

Formula

a(n) = prime(n)^((prime(n)-3)/2).

Extensions

More terms from Franklin T. Adams-Watters, Jan 24 2012