A334989 Perimeters of Heronian triangles where the lengths of the smallest and middle sides are coprime.

12, 30, 32, 36, 40, 42, 44, 48, 50, 54, 56, 60, 64, 66, 68, 70, 72, 76, 78, 80, 84, 90, 96, 98, 100, 104, 108, 110, 112, 114, 120, 126, 128, 130, 132, 136, 140, 144, 150, 152, 154, 156, 160, 162, 164, 168, 170, 172, 174, 176, 180, 182, 186, 190, 192, 196, 198, 200, 204

Offset

1,1

Comments

This sequence includes the perimeters of all primitive Heronian triangles (A096468). First differs from A096468 at a(2) = 30.

Links

Table of n, a(n) for n=1..59.

Eric Weisstein's World of Mathematics, Heronian Triangle

Wikipedia, Heronian triangle

Wikipedia, Integer Triangle

Example

a(1) = 12; there is one Heronian triangle with perimeter 12, which is [3,4,5] and the lengths of the smallest and middle sides are coprime (GCD(3,4) = 1).
a(3) = 32; there is one Heronian triangle with perimeter 32, [4,13,15] and the lengths of the smallest and middle sides are coprime (GCD(4,13) = 1).

Crossrefs

Cf. A051518, A096468, A334983, A334984.

Sequence in context: A183723 A247152 A299041 * A331367 A335149 A050689

Adjacent sequences: A334986 A334987 A334988 * A334990 A334991 A334992

Keyword

nonn

Author

Wesley Ivan Hurt, May 18 2020

Status

approved