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Perimeters of Heronian triangles where the lengths of the smallest and largest sides are coprime.
2

%I #13 Feb 01 2021 18:14:52

%S 12,16,18,30,32,36,40,42,44,48,50,54,56,60,64,66,68,70,72,76,78,80,84,

%T 90,96,98,100,104,108,110,112,114,120,126,128,130,132,140,144,150,152,

%U 154,156,160,162,164,168,170,172,174,176,180,182,186,190,192,196,198,200,204

%N Perimeters of Heronian triangles where the lengths of the smallest and largest sides are coprime.

%C This sequence includes the perimeters of all primitive Heronian triangles (A096468). First differs from A096468 at a(38) = 140.

%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, which is [3,4,5] and the lengths of the smallest and largest sides are coprime (GCD(3,5) = 1).

%e a(5) = 32; there is one Heronian triangle with perimeter 32, [4,13,15] and the lengths of the smallest and middle sides are coprime (GCD(4,13) = 1).

%Y Cf. A051518, A096468, A334984, A334989.

%K nonn

%O 1,1

%A _Wesley Ivan Hurt_, May 18 2020

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Last modified September 20 18:47 EDT 2024. Contains 376075 sequences. (Running on oeis4.)