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A334791 Perimeters of Pythagorean triangles with squarefree area. 1
12, 30, 70, 84, 132, 182, 260, 340, 374, 390, 420, 462, 476, 494, 510, 598, 646, 782, 798, 870, 966, 1012, 1054, 1254, 1276, 1302, 1334, 1508, 1518, 1612, 1628, 1716, 1804, 1860, 1892, 1924, 2030, 2046, 2132, 2220, 2262, 2310, 2380, 2444, 2460, 2494, 2516, 2542 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..10000

Wikipedia, Integer Triangle

Index entries related to Pythagorean Triples.

EXAMPLE

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

MATHEMATICA

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 *)

CROSSREFS

Cf. A010814.

Sequence in context: A323441 A064483 A322181 * A110019 A069486 A211117

Adjacent sequences:  A334788 A334789 A334790 * A334792 A334793 A334794

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, May 10 2020

EXTENSIONS

Terms a(39) and beyond from Giovanni Resta, May 11 2020

STATUS

approved

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Last modified March 7 11:45 EST 2021. Contains 341869 sequences. (Running on oeis4.)