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Search: id:A094807
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| A094807 |
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Numbers n such that primitive solutions for 1/n^2 = 1/x^2 + 1/y^2 exist. |
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2
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| 12, 60, 120, 168, 360, 420, 660, 1008, 1092, 1260, 1680, 1848, 1980, 2448, 2640, 2772, 3120, 3420, 3432, 4620, 4680, 5148, 5460, 6072, 7140, 7800, 8160, 8580, 9240, 9828, 10032, 11220, 11628, 12180, 13260, 14280, 14880, 15708, 15912, 15960, 17940
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OFFSET
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1,1
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COMMENT
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Numbers n that are the product of two legs of a primitive Pythagorean triangle, that is, n = 2xy(x^2-y^2) where x and y are two relatively prime positive integers of different parity and x is greater than y.
Numbers n which are the length of the altitude on the hypotenuse of a Pythagorean triangle and the smallest in its similarity class.
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REFERENCES
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E. Bahier, Recherche Methodique et Proprietes des Triangles Rectangles en Nombres Entiers, Hermann, Paris, 1916. p. 68.
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FORMULA
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Equals 2*A024365(n).
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EXAMPLE
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12 is in the sequence because we have 1/12^2 = 1/15^2 + 1/20^2 and gcd(12,15,20)=1.
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CROSSREFS
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Sequence in context: A012657 A012406 A097191 this_sequence A120644 A099829 A099830
Adjacent sequences: A094804 A094805 A094806 this_sequence A094808 A094809 A094810
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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), Jun 11 2004
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EXTENSIONS
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Comments provided by Michael Somos, Oct 01 2004
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