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

Author

N. J. A. Sloane, Jun 09 2000

Keywords

• nonn
• easy
• nice

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

Crossrefs

Cf. A055669 (zeros removed), A055670, A055671, A055672.

Programs

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 *)

Formula

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

Extensions

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