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Search: id:A072289
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| A072289 |
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One eighty-fourth the area of primitive Pythagorean triangles with (increasing) square hypotenuses (precisely those of A008846). |
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1
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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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.
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CROSSREFS
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Cf. A020882.
Sequence in context: A037979 A044417 A044798 this_sequence A027524 A043340 A045129
Adjacent sequences: A072286 A072287 A072288 this_sequence A072290 A072291 A072292
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KEYWORD
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nonn
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AUTHOR
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Lekraj Beedassy (blekraj(AT)yahoo.com), Jul 11 2002
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EXTENSIONS
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Corrected and extended by Ray Chandler (rayjchandler(AT)sbcglobal.net), Oct 28 2003
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