A392942 Distinct semiperimeters of triangles with integer sides, integer area, and integer circumradius.

12, 24, 30, 36, 40, 42, 48, 54, 56, 60, 64, 70, 72, 80, 84, 90, 96, 104, 108, 110, 112, 120, 126, 128, 132, 140, 144, 150, 154, 156, 160, 162, 168, 176, 180, 182, 192, 198, 200, 204, 208, 210, 216, 220, 224, 228, 234, 238, 240, 250, 252, 256, 260, 264, 270, 276

Offset

1,1

Links

Table of n, a(n) for n=1..56.

Eric Weisstein's World of Mathematics, Circumradius.

Eric Weisstein's World of Mathematics, Heronian Triangle.

Example

The triangle (14, 30, 40) with semiperimeter (14 + 30 + 40) = 42 has area sqrt(42*(42 - 14)*(42 - 30)*(42 - 40)) = 168 and circumradius (14*30*40)/(4*168) = 25, hence 42 is a term.

Maple

A392942 := proc(n)
    option remember;
    local f, k, x, y, z;
    if n = 1 then 12 else
        for k from A392942(n - 1) + 1 do
            for x to 2*k/3 do
                for y from max(x, k - x + 1) to k - x/2 do
                    z := 2*k - x - y;
                    f := k*(k - x)*(k - y)*(k - z);
                    if issqr(f) and x*y*z mod (4*isqrt(f)) = 0 then
                        return k;
                    end if;
                end do;
            end do;
        end do;
    end if;
end proc:
seq(A392942(n), n = 1 .. 56);

Crossrefs

Subsequence of A305704.

Cf. A070201, A208984, A210207, A228383, A392943.

Sequence in context: A333945 A335146 A365008 * A182225 A074697 A333919

Adjacent sequences: A392939 A392940 A392941 * A392943 A392944 A392945

Keyword

nonn

Author

Felix Huber, Feb 04 2026

Status

approved