A094807 Numbers n such that primitive solutions for 1/n^2 = 1/x^2 + 1/y^2 exist.

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

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..41.

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

Sequence in context: A097191 A338159 A273691 * A120644 A099829 A099830

Adjacent sequences: A094804 A094805 A094806 * A094808 A094809 A094810

Keyword

nonn

Author

Lekraj Beedassy, Jun 11 2004

Extensions

Comments provided by Michael Somos, Oct 01 2004

Status

approved