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A334761 Perimeters of Pythagorean triangles whose hypotenuse divides the difference of squares of its long and short legs. 3

%I

%S 60,120,180,240,300,360,390,420,480,540,600,660,680,720,780,840,900,

%T 960,1020,1080,1140,1170,1200,1260,1320,1360,1380,1400,1440,1500,1560,

%U 1620,1680,1740,1800,1860,1920,1950,1980,2030,2040,2100,2160,2220,2280,2340,2400

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

%C 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

%H Giovanni Resta, <a href="/A334761/b334761.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 Wikipedia, <a href="http://en.wikipedia.org/wiki/Pythagorean_triple">Pythagorean Triple</a>.

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

%e 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.

%t 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 *)

%Y Cf. A005044, A010814.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, May 10 2020

%E Terms a(31) and beyond from _Giovanni Resta_, May 11 2020

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Last modified April 16 12:45 EDT 2021. Contains 343037 sequences. (Running on oeis4.)