cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

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

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Author

Lekraj Beedassy, Jul 11 2002

Keywords

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