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A055671 Number of prime Hurwitz quaternions of norm n. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Oct 03 2012 *)

CROSSREFS

Cf. A055669-A055672.

Sequence in context: A076799 A297540 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

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Last modified August 10 00:32 EDT 2022. Contains 356026 sequences. (Running on oeis4.)