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A057228
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a(n) = u * v = x * y with (u - v) = (x + y) = A009000(n) (u>v, y>0, v>0, x>0, y>0).
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1
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6, 24, 30, 54, 60, 96, 84, 150, 120, 210, 216, 240, 294, 210, 270, 384, 180, 486, 336, 600, 540, 480, 630, 726, 840, 864, 330, 504, 750, 924, 1014, 960, 1176, 1320, 840, 756, 1350, 1080, 1536, 720, 546, 1386, 1500, 1734, 1890, 1560, 1944, 1470, 2166
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OFFSET
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1,1
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COMMENTS
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Areas of Pythagorean triangles.
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LINKS
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EXAMPLE
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a(1) = 6 = 6 * 1 = 3 * 2, (6 - 1)=(3 + 2) = 5 = A009000(1).
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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