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%I #9 Nov 03 2019 17:12:02
%S 1,2,0,2,1,2,1,2,1,4,1,1,0,4,2,2,0,2,1,4,3,1,0,2,1,2,0,4,0,2,0,2,1,1,
%T 6,3,0,0,1,5,0,3,0,3,2,0,0,2,1,4,1,0,0,2,4,8,0,0,0,5,0,0,1,2,1,3,0,1,
%U 0,15,0,2,0,0,0,4,2,1,0,5,1,0,0,6,2,0,1,3,0,4,3,0,0,0,1,2,0,2,1,2,0,0,0
%N Number of integer-sided triangles of area 6n.
%C If integer-sided triangle has integer area, area is divisible by 6.
%H Giovanni Resta, <a href="/A051585/b051585.txt">Table of n, a(n) for n = 1..10000</a>
%o (PARI) a(n)=sum(z=sqrtint(sqrtint(192*n^2)-1)+1,sqrtint(9*(64*n^2+5)\20), sum(y=z\2+1,z, my(t=(y*z)^2-(12*n)^2,x); if(issquare(t,&t), (issquare(y^2+z^2-2*t,&x) && x<=y) + (t && issquare(y^2+z^2+2*t,&x) && x<=y), 0))) \\ _Charles R Greathouse IV_, Jun 27 2013
%Y Cf. A051584, A051586.
%K nonn
%O 1,2
%A _David W. Wilson_
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