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A072289 One eighty-fourth the area of primitive Pythagorean triangles with (increasing) square hypotenuses (precisely those of A008846). 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 9 19:51 EST 2019. Contains 329879 sequences. (Running on oeis4.)