A331241 Integer values that can be assumed by the squared radius of the circumcircle of a triangle with integer sides.

3, 12, 25, 27, 48, 75, 100, 108, 112, 147, 162, 169, 192, 225, 240, 243, 289, 300, 363, 400, 405, 432, 448, 507, 588, 625, 648, 675, 676, 768, 841, 867, 891, 900, 960, 972

Offset: 1

Author

Hugo Pfoertner, Jan 13 2020

Keywords

• nonn
• more

Comments

Values of A331227(k) at positions k for which A331228(k) = 1.

Examples

			a(1) = 3, because the triangle with sides (3,3,3) is the first triangle for which R^2 has an integer value.
a(2) = 12: (6,6,6),
a(3) = 25: (6,8,10) scaled-up Pythagorean triangle (3,4,5),
a(4) = 27: (9,9,9),
a(5) = 48: (12,12,12),
...
a(10) = 147: (9,15,21).
		

Crossrefs

Cf. A331227, A331228.

Formula

Squared radius of circumcircle of triangle with sides a, b, c:

R^2 = (a*b*c)^2 / (16*s*(s - a)*(s - b)*(s - c)) with s = (a + b + c)/2.