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

Author

Lekraj Beedassy, Jun 11 2004

Keywords

• nonn

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.

Examples

			12 is in the sequence because we have 1/12^2 = 1/15^2 + 1/20^2 and gcd(12,15,20)=1.
		

References

• E. Bahier, Recherche Methodique et Proprietes des Triangles Rectangles en Nombres Entiers, Hermann, Paris, 1916. p. 68.

Formula

Equals 2*A024365(n).

Extensions

Comments provided by Michael Somos, Oct 01 2004