A334791 Perimeters of Pythagorean triangles with squarefree area.

12, 30, 70, 84, 132, 182, 260, 340, 374, 390, 420, 462, 476, 494, 510, 598, 646, 782, 798, 870, 966, 1012, 1054, 1254, 1276, 1302, 1334, 1508, 1518, 1612, 1628, 1716, 1804, 1860, 1892, 1924, 2030, 2046, 2132, 2220, 2262, 2310, 2380, 2444, 2460, 2494, 2516, 2542

Offset: 1

Author

Wesley Ivan Hurt, May 10 2020

Keywords

• nonn

Comments

The smallest terms corresponding to 2, 3, and 4 triangles are a(32) = 1716, a(1325) = 81510, and a(5027) = 317460, respectively. - Giovanni Resta, May 11 2020

Examples

			a(1) = 12; There is one Pythagorean triangle, [3,4,5], with perimeter 12 whose area 3*4/2 = 6 (squarefree).
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• Wikipedia, Integer Triangle
• Index entries related to Pythagorean Triples.

Crossrefs

Cf. A010814.

Programs

Mathematica

Reap[ Do[s = Solve[ x^2 + y^2 == (p-x-y)^2 && 0 0, {x, y}, Integers]; If[s != {} && AnyTrue[x y/2 /. s, SquareFreeQ], Print@ Sow@ p], {p, 12, 1000, 2}]][[2, 1]] (* Giovanni Resta, May 11 2020 *)

Extensions

Terms a(39) and beyond from Giovanni Resta, May 11 2020