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

1,1

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

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Wikipedia, Integer Triangle

Index entries related to Pythagorean Triples.

Example

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

Mathematica

Reap[ Do[s = Solve[ x^2 + y^2 == (p-x-y)^2 && 0<x<y && p-x-y > 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 *)

Crossrefs

Cf. A010814.

Sequence in context: A064483 A365277 A322181 * A110019 A069486 A211117

Adjacent sequences: A334788 A334789 A334790 * A334792 A334793 A334794

Keyword

nonn

Author

Wesley Ivan Hurt, May 10 2020

Extensions

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

Status

approved