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

1,1

Comments

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

Links

Table of n, a(n) for n=1..36.

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.

Example

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.

Sequence in context: A206917 A320334 A009776 * A068967 A071355 A366984

Adjacent sequences: A331238 A331239 A331240 * A331242 A331243 A331244

Keyword

nonn,more

Author

Hugo Pfoertner, Jan 13 2020

Status

approved