A055671 Number of prime Hurwitz quaternions of norm n.

0, 0, 24, 96, 0, 144, 0, 192, 0, 0, 0, 288, 0, 336, 0, 0, 0, 432, 0, 480, 0, 0, 0, 576, 0, 0, 0, 0, 0, 720, 0, 768, 0, 0, 0, 0, 0, 912, 0, 0, 0, 1008, 0, 1056, 0, 0, 0, 1152, 0, 0, 0, 0, 0, 1296, 0, 0, 0, 0, 0, 1440, 0, 1488, 0, 0, 0, 0, 0, 1632, 0, 0, 0, 1728, 0, 1776, 0, 0, 0, 0, 0

Offset

0,3

References

L. E. Dickson, Algebras and Their Arithmetics, Dover, 1960, Section 91.

Links

R. J. Mathar, Table of n, a(n) for n = 0..10000

Formula

a(n) = number of vectors of norm n in D_4 lattice (A004011) if n is a prime, otherwise a(n) = 0.

Mathematica

a[p_?PrimeQ] := Reduce[ a^2 + b^2 + c^2 + d^2 == 4p, {a, b, c, d}, Integers] // Length; a[_] = 0; Table[ a[n], {n, 0, 78}] (* Jean-François Alcover, Oct 03 2012 *)

Crossrefs

Cf. A055669-A055672.

Sequence in context: A297540 A365191 A353326 * A090214 A283446 A208984

Adjacent sequences: A055668 A055669 A055670 * A055672 A055673 A055674

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Jun 09 2000

Extensions

More terms from Lambert Klasen (Lambert.Klasen(AT)gmx.net), Jun 10 2005

Status

approved