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%I #12 Nov 21 2013 12:48:19
%S 0,1,0,0,1,0,1,1,0,1,0,0,2,1,0,1,2,1,1,0,1,0,2,3,1,3,0,2,1,2,0,3,2,2,
%T 3,0,1,1,0,3,3,2,0,1,2,0,2,0,3,2,3,0,3,4,4,0,5,0,1,5,2,4,2,0,2,2,2,2,
%U 3,3,4,0,0,2,2,0,5,1,5,4,5,2,0,3,0,3,5,2,7,0,4,0,0,5,2,0,7,8,3,2,2,4,5,8,3
%N Number of ways that prime(n) can be represented as a^2+b^2+c^2 with c >= b >= a > 0.
%H T. D. Noe, <a href="/A094713/b094713.txt">Table of n, a(n) for n=1..10000</a>
%e a(13) = 2 because prime(13) = 41 = 1+4+36 = 9+16+16.
%t lim=25; pLst=Table[0, {PrimePi[lim^2]}]; Do[n=a^2+b^2+c^2; If[n<lim^2 && PrimeQ[n], pLst[[PrimePi[n]]]++ ], {a, lim}, {b, a, Sqrt[lim^2-a^2]}, {c, b, Sqrt[lim^2-a^2-b^2]}; pLst
%t Table[Count[PowersRepresentations[Prime[n],3,2], _?(Min[#]>0&)],{n,110}] (* _Harvey P. Dale_, Feb 17 2011 *)
%Y Cf. A085317 (primes that are the sum of three positive squares), A094712 (primes that are not the sum of three positive squares), A094714 (least prime having exactly n representations as the sum of three positive squares).
%K nonn
%O 1,13
%A _T. D. Noe_, May 21 2004
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