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%I #13 Oct 23 2016 12:53:08
%S 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,
%T 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,
%U 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
%N Number of right-inequivalent prime Hurwitz quaternions of norm n.
%C Two primes are considered right-equivalent if they differ by right multiplication by one of the 24 units.
%D L. E. Dickson, Algebras and Their Arithmetics, Dover, 1960, Section 91.
%H R. J. Mathar, <a href="/A055672/b055672.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = A055671(n)/24.
%t 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 *)
%Y Cf. A055669-A055671.
%K nonn,easy,nice
%O 0,4
%A _N. J. A. Sloane_, Jun 09 2000
%E 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.
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