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A334761 Perimeters of Pythagorean triangles whose hypotenuse divides the difference of squares of its long and short legs. 3
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 (list; graph; refs; listen; history; text; internal format)
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.

Index to sequences related to Pythagorean Triples.

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

Cf. A005044, A010814.

Sequence in context: A056866 A098136 A060793 * A169823 A309842 A177871

Adjacent sequences:  A334758 A334759 A334760 * A334762 A334763 A334764

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 10 2020

EXTENSIONS

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

STATUS

approved

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Last modified March 5 16:55 EST 2021. Contains 341827 sequences. (Running on oeis4.)