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A331241
Integer values that can be assumed by the squared radius of the circumcircle of a triangle with integer sides.
0
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.
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
Sequence in context: A206917 A320334 A009776 * A068967 A071355 A366984
KEYWORD
nonn,more
AUTHOR
Hugo Pfoertner, Jan 13 2020
STATUS
approved