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A334791 Perimeters of Pythagorean triangles with squarefree area. 1

%I #12 Jun 16 2020 14:44:07

%S 12,30,70,84,132,182,260,340,374,390,420,462,476,494,510,598,646,782,

%T 798,870,966,1012,1054,1254,1276,1302,1334,1508,1518,1612,1628,1716,

%U 1804,1860,1892,1924,2030,2046,2132,2220,2262,2310,2380,2444,2460,2494,2516,2542

%N Perimeters of Pythagorean triangles with squarefree area.

%C 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

%H Giovanni Resta, <a href="/A334791/b334791.txt">Table of n, a(n) for n = 1..10000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Integer_triangle">Integer Triangle</a>

%H <a href="/index/Ps#PyTrip">Index entries related to Pythagorean Triples.</a>

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

%t 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 *)

%Y Cf. A010814.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, May 10 2020

%E Terms a(39) and beyond from _Giovanni Resta_, May 11 2020

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)