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

2,2

Links

Table of n, a(n) for n=2..15.

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.

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A152291.

Sequence in context: A075986 A251657 A084765 * A218322 A247707 A082795

Adjacent sequences: A203408 A203409 A203410 * A203412 A203413 A203414

Keyword

nonn

Author

Franz Vrabec, Jan 01 2012

Extensions

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

Status

approved