A192493 Numerators of squared radii of circumcircles of non-degenerate triangles with integer vertex coordinates.

1, 1, 5, 25, 25, 2, 5, 25, 25, 13, 325, 169, 65, 4, 65, 17, 425, 221, 9, 289, 1105, 169, 85, 5, 325, 85, 50, 1105, 289, 25, 2125, 625, 13, 325, 425, 1625, 169, 1105, 125, 65, 29, 2465, 4225, 1885, 725, 377, 2465, 5525, 1885, 125, 8, 145, 65, 841, 17, 841, 845, 425, 2125, 221, 6409, 9425, 9, 325, 289, 145, 1105, 37, 5365, 3145, 169, 2405, 925, 85, 1369, 4625, 481, 625, 493, 2405, 10

Offset: 1

Author

Hugo Pfoertner, Jul 10 2011

Keywords

• nonn
• frac

Examples

			The smallest triangle of lattice points {(0,0),(1,0),(0,1)} has circumradius R=sqrt(2)/2, i.e., R^2=1/2. Therefore a(1)=1, A192494(1)=2.
		

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..9089, covering range R^2 <= 100.
• Hugo Pfoertner, Circles Passing through 3 Points of the Square Lattice, illustrations up to R^2=10.

Crossrefs

Cf. A192494 (corresponding denominators), A128006, A128007.

Cf. A346993, A346994, A346995.