A057228 a(n) = u * v = x * y with (u - v) = (x + y) = A009000(n) (u>v, y>0, v>0, x>0, y>0).

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

Offset

1,1

Comments

Areas of Pythagorean triangles.

Links

David A. Corneth, Table of n, a(n) for n = 1..10000

Example

a(1) = 6 = 6 * 1 = 3 * 2, (6 - 1)=(3 + 2) = 5 = A009000(1).

Prog

(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

Crossrefs

Cf. A009000, A009003, A009111, A009112.

Sequence in context: A009111 A009112 A057101 * A334788 A332962 A350564

Adjacent sequences: A057225 A057226 A057227 * A057229 A057230 A057231

Keyword

nonn

Author

Naohiro Nomoto, Sep 19 2000

Extensions

Offset changed to 1 by David A. Corneth, Apr 10 2021

Status

approved