A072289 One eighty-fourth the area of primitive Pythagorean triangles with (increasing) square hypotenuses (precisely those of A008846).

1, 85, 230, 1054, 205, 5405, 6510, 18615, 27335, 44556, 45034, 22660, 89531, 152889, 181220, 53430, 221595, 304265, 246380, 720291, 360910, 595884, 811954, 1444915, 1362295, 40630, 2504645, 1304445, 2385474, 3311396, 3647810, 2420665, 1641809

Offset: 1

Author

Lekraj Beedassy, Jul 11 2002

Keywords

• nonn

Comments

For Pythagorean triples (x, y, z) satisfying x^2 + y^2 = z^2, we have 3 and 4 dividing either of x or y and 7 dividing x, y or (x^2 - y^2), so that 3*4*7 always divide x*y*(x^2 - y^2); if (x, y) be themselves the generators of another Pythagorean triple, (x^2 - y^2, 2*x*y, x^2 + y^2=z^2), the corresponding primitive Pythagorean triangle has area x*y*(x^2 - y^2) and is hence divisible by 84.

Crossrefs

Cf. A020882.

Extensions

Corrected and extended by Ray Chandler, Oct 28 2003

Sorted by increasing square hypotenuse, then increasing area by Sean A. Irvine, Sep 20 2024