|
Search: id:A094807
|
|
|
| A094807 |
|
Numbers n such that primitive solutions for 1/n^2 = 1/x^2 + 1/y^2 exist. |
|
+0
2
|
|
| 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
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
COMMENT
|
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.
|
|
REFERENCES
|
E. Bahier, Recherche Methodique et Proprietes des Triangles Rectangles en Nombres Entiers, Hermann, Paris, 1916. p. 68.
|
|
FORMULA
|
Equals 2*A024365(n).
|
|
EXAMPLE
|
12 is in the sequence because we have 1/12^2 = 1/15^2 + 1/20^2, and gcd(12,15,20)=1.
|
|
CROSSREFS
|
Adjacent sequences: A094804 A094805 A094806 this_sequence A094808 A094809 A094810
Sequence in context: A012657 A012406 A097191 this_sequence A120644 A099829 A099830
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Lekraj Beedassy (blekraj(AT)yahoo.com), Jun 11 2004
|
|
EXTENSIONS
|
Comments provided by Michael Somos, Oct 01 2004
|
|
|
Search completed in 0.002 seconds
|
