A334761 Perimeters of Pythagorean triangles whose hypotenuse divides the difference of squares of its long and short legs.

60, 120, 180, 240, 300, 360, 390, 420, 480, 540, 600, 660, 680, 720, 780, 840, 900, 960, 1020, 1080, 1140, 1170, 1200, 1260, 1320, 1360, 1380, 1400, 1440, 1500, 1560, 1620, 1680, 1740, 1800, 1860, 1920, 1950, 1980, 2030, 2040, 2100, 2160, 2220, 2280, 2340, 2400

Offset: 1

Author

Wesley Ivan Hurt, May 10 2020

Keywords

• nonn

Comments

The smallest terms corresponding to 2,...,5 triangles are a(15) = 780, a(191) = 9360, a(3324) = 159120, and a(19433) = 928200, respectively. - Giovanni Resta, May 11 2020

Examples

			a(1) = 60; the triangle [15,20,25] has perimeter 60. The difference of squares of its long and short leg lengths is (20^2 - 15^2) = 400 - 225 = 175 and 25|175.
		

Links

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

Crossrefs

Cf. A005044, A010814.

Programs

Mathematica

Reap[Do[s = Solve[x^2 + y^2 == (p-x-y)^2 && z^2 == x^2 + y^2 && 0 0, {x, y, z}, Integers]; If[s != {} && AnyTrue[{x, y , z} /. s, Mod[#[[2]]^2 - #[[1]]^2, #[[3]]] == 0 &], Print@Sow@p], {p, 12, 1000, 2}]][[2, 1]] (* Giovanni Resta, May 11 2020 *)

Extensions

Terms a(31) and beyond from Giovanni Resta, May 11 2020