A055672 Number of right-inequivalent prime Hurwitz quaternions of norm n.

0, 0, 1, 4, 0, 6, 0, 8, 0, 0, 0, 12, 0, 14, 0, 0, 0, 18, 0, 20, 0, 0, 0, 24, 0, 0, 0, 0, 0, 30, 0, 32, 0, 0, 0, 0, 0, 38, 0, 0, 0, 42, 0, 44, 0, 0, 0, 48, 0, 0, 0, 0, 0, 54, 0, 0, 0, 0, 0, 60, 0, 62, 0, 0, 0, 0, 0, 68, 0, 0, 0, 72, 0, 74, 0, 0, 0, 0, 0, 80, 0, 0, 0, 84, 0, 0, 0, 0, 0, 90

Offset

0,4

Comments

Two primes are considered right-equivalent if they differ by right multiplication by one of the 24 units.

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) = A055671(n)/24.

Mathematica

A055671[n_] := If[PrimeQ[n], Reduce[a^2 + b^2 + c^2 + d^2 == 4n, {a, b, c, d}, Integers] // Length, 0]; a[n_] := A055671[n]/24; Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Oct 22 2016 *)

Crossrefs

Cf. A055669-A055671.

Sequence in context: A178105 A178109 A339873 * A327964 A085562 A037282

Adjacent sequences: A055669 A055670 A055671 * A055673 A055674 A055675

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, Jun 09 2000

Extensions

I would also like to get the sequences of inequivalent prime Hurwitz quaternions, where two primes are considered equivalent if they differ by left or right multiplication by one of the 24 units. This will give two more sequences, analogs of A055670 and A055672.

Status

approved