A331241 - OEIS

%I #9 Jan 13 2020 22:31:15

%S 3,12,25,27,48,75,100,108,112,147,162,169,192,225,240,243,289,300,363,

%T 400,405,432,448,507,588,625,648,675,676,768,841,867,891,900,960,972

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

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

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

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

%e a(1) = 3, because the triangle with sides (3,3,3) is the first triangle for which R^2 has an integer value.

%e a(2) = 12: (6,6,6),

%e a(3) = 25: (6,8,10) scaled-up Pythagorean triangle (3,4,5),

%e a(4) = 27: (9,9,9),

%e a(5) = 48: (12,12,12),

%e ...

%e a(10) = 147: (9,15,21).

%Y Cf. A331227, A331228.

%K nonn,more

%O 1,1

%A _Hugo Pfoertner_, Jan 13 2020