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, 45034, 44556, 22660, 152889, 89531, 181220, 53430, 221595, 304265, 246380, 720291, 360910, 595884, 811954, 1444915, 1362295, 40630, 2504645, 1304445, 3311396, 2385474, 3647810, 2420665, 1641809

Offset

1,2

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.

Links

Table of n, a(n) for n=1..33.

Crossrefs

Cf. A020882.

Sequence in context: A044417 A044798 A260100 * A211257 A027524 A043340

Adjacent sequences: A072286 A072287 A072288 * A072290 A072291 A072292

Keyword

nonn

Author

Lekraj Beedassy, Jul 11 2002

Extensions

Corrected and extended by Ray Chandler, Oct 28 2003

Status

approved