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Largest possible area of a primitive Heronian triangle with perimeter A096468(n).
0

%I #8 Jun 18 2020 14:02:03

%S 6,12,12,30,24,60,60,84,66,84,120,126,84,60,168,132,204,210,84,114,

%T 156,180,252,360,264,420,420,468,306,330,504,456,420,630,720,780,660,

%U 408,630,660,1020,456,924,1170,840,1260,984,924,1020,1290,522,1320,420,1092,1116,1710

%N Largest possible area of a primitive Heronian triangle with perimeter A096468(n).

%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) = 6; there is one primitive Heronian triangle with perimeter A096468(1) = 12, which is [3,4,5] and its area is 6.

%e a(6) = 60; there are two primitive Heronian triangles with perimeter A096468(6) = 36, [9,10,17] and [10,13,13] with areas 36 and 60. The largest of these is 60.

%Y Cf. A096468.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, May 03 2020