A334120 -id:A334120 - cp's OEIS frontend

A330874 Sum of the smallest side lengths of all primitive Heronian triangles with perimeter A096468(n).

3, 5, 5, 5, 4, 19, 8, 20, 11, 10, 29, 28, 7, 6, 36, 11, 17, 37, 8, 19, 15, 29, 69, 47, 15, 133, 64, 38, 71, 25, 100, 25, 25, 28, 97, 39, 132, 20, 46, 84, 142, 19, 103, 93, 67, 242, 41, 40, 34, 43, 29, 179, 41, 76, 70, 95, 267, 301, 69, 192, 119, 68, 178, 136, 99, 61, 201, 218

Offset: 1

Wesley Ivan Hurt, May 16 2020

nonn

			a(1) = 3; there is one primitive Heronian triangle with perimeter A096468(1) = 12, [3,4,5] and 3 is the smallest side length.
a(6) = 19; there are two primitive Heronian triangles with perimeter A096468(6) = 36, [9,10,17] and [10,13,13]. The sum of the smallest side lengths is then 9 + 10 = 19.

Eric Weisstein's World of Mathematics, Heronian Triangle
Wikipedia, Heronian triangle
Wikipedia, Integer Triangle

Cf. A096468, A334018, A334120.

A334018 Sum of the middle side lengths of all primitive Heronian triangles with perimeter A096468(n).

Original entry on oeis.org

4, 5, 5, 12, 13, 23, 15, 29, 13, 17, 30, 62, 24, 25, 71, 25, 25, 46, 29, 20, 26, 55, 160, 106, 37, 205, 109, 79, 209, 33, 146, 38, 39, 45, 195, 41, 296, 51, 178, 226, 266, 60, 153, 172, 105, 486, 50, 51, 61, 61, 60, 297, 50, 214, 130, 130, 476, 565, 252, 258, 192, 158, 493

Offset: 1

Wesley Ivan Hurt, May 16 2020

nonn

			a(1) = 4; there is one primitive Heronian triangle with perimeter A096468(1) = 12, [3,4,5] and 4 is the middle side length.
a(6) = 23; there are two primitive Heronian triangles with perimeter A096468(6) = 36, [9,10,17] and [10,13,13]. The sum of the middle side lengths is then 10 + 13 = 23.

Eric Weisstein's World of Mathematics, Heronian Triangle
Wikipedia, Heronian triangle
Wikipedia, Integer Triangle

Cf. A096468, A330874, A334120.

cp's OEIS Frontend

A330874 Sum of the smallest side lengths of all primitive Heronian triangles with perimeter A096468(n).

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