OFFSET
1,1
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
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
Wikipedia, Integer Triangle
Wikipedia, Pythagorean Triple.
EXAMPLE
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.
MATHEMATICA
Reap[Do[s = Solve[x^2 + y^2 == (p-x-y)^2 && z^2 == x^2 + y^2 && 0<x<y<z && p - x - y > 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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 10 2020
EXTENSIONS
Terms a(31) and beyond from Giovanni Resta, May 11 2020
STATUS
approved