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%I #17 Apr 10 2021 22:28:32
%S 6,24,30,54,60,96,84,150,120,210,216,240,294,210,270,384,180,486,336,
%T 600,540,480,630,726,840,864,330,504,750,924,1014,960,1176,1320,840,
%U 756,1350,1080,1536,720,546,1386,1500,1734,1890,1560,1944,1470,2166
%N a(n) = u * v = x * y with (u - v) = (x + y) = A009000(n) (u>v, y>0, v>0, x>0, y>0).
%C Areas of Pythagorean triangles.
%H David A. Corneth, <a href="/A057228/b057228.txt">Table of n, a(n) for n = 1..10000</a>
%e a(1) = 6 = 6 * 1 = 3 * 2, (6 - 1)=(3 + 2) = 5 = A009000(1).
%o (PARI) list(lim) = {my(lh = List()); for(u = 2, sqrtint(lim), for(v = 1, u, if (u^2+v^2 > lim, break); if ((gcd(u, v) == 1) && (0 != (u-v)%2), for (i = 1, lim, if (i*(u^2+v^2) > lim, break); /* if (u^2 - v^2 < 2*u*v, w = [i*(u^2 - v^2), i*2*u*v, i*(u^2+v^2)], w = [i*2*u*v, i*(u^2 - v^2), i*(u^2+v^2)]); */ listput(lh, [i*(u^2+v^2), i^2*(u^2 - v^2)*u*v]); ); ); ); ); lh = vecsort(Vec(lh)); vector(#lh, i, lh[i][2])} \\ _David A. Corneth_, Apr 10 2021, adapted from A009000
%Y Cf. A009000, A009003, A009111, A009112.
%K nonn
%O 1,1
%A _Naohiro Nomoto_, Sep 19 2000
%E Offset changed to 1 by _David A. Corneth_, Apr 10 2021
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