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%I #11 Aug 24 2019 11:52:24
%S 0,0,0,0,0,1,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,1,0,0,0,0,
%T 0,2,0,0,0,0,0,1,0,0,0,0,0,2,0,0,0,0,0,1,0,0,0,0,0,4,0,0,0,0,0,1,0,0,
%U 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,4,0,0,0,0,0,2,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,1,0,0,0,0,0,4
%N Number of integer-sided triangles of area n.
%C If integer-sided triangle has integer area, area is divisible by 6.
%H Antti Karttunen, <a href="/A051584/b051584.txt">Table of n, a(n) for n = 1..10085</a>
%o (PARI)
%o A051585(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))); \\ From A051585 by _Charles R Greathouse IV_
%o A051584(n) = if((n%6),0,A051585(n/6)); \\ _Antti Karttunen_, Aug 23 2019
%Y Cf. A051585, A051586.
%K nonn
%O 1,12
%A _David W. Wilson_
%E Data section extended up to a(120) by _Antti Karttunen_, Aug 23 2019
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