A192493 - OEIS

%I #33 Aug 24 2021 21:09:44

%S 1,1,5,25,25,2,5,25,25,13,325,169,65,4,65,17,425,221,9,289,1105,169,

%T 85,5,325,85,50,1105,289,25,2125,625,13,325,425,1625,169,1105,125,65,

%U 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

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

%H Hugo Pfoertner, <a href="/A192493/b192493.txt">Table of n, a(n) for n = 1..9089</a>, covering range R^2 <= 100.

%H Hugo Pfoertner, <a href="/A192493/a192493.pdf">Circles Passing through 3 Points of the Square Lattice</a>, illustrations up to R^2=10.

%e 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.

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

%Y Cf. A346993, A346994, A346995.

%K nonn,frac

%O 1,3

%A _Hugo Pfoertner_, Jul 10 2011