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Perimeters of Heronian triangles with squarefree area.
5

%I #16 Jun 16 2020 13:03:14

%S 12,30,42,44,70,76,84,100,110,132,140,150,154,156,172,182,186,196,204,

%T 220,228,230,236,238,242,252,260,268,294,300,308,318,322,330,340,350,

%U 364,372,374,380,390,396,420,428,444,462,468,470,476,484,490,492,494,506,510

%N Perimeters of Heronian triangles with squarefree area.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Heronian_triangle">Heronian triangle</a>

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

%e a(1) = 12; there is one Heronian triangle with perimeter 12 whose area is squarefree, which is [3,4,5] with area 6.

%e a(2) = 30; there is one Heronian triangle with a perimeter of 30 whose area is squarefree, which is [5,12,13] with area 30.

%Y Cf. A330869, A334538.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, May 05 2020