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A334984
Perimeters of Heronian triangles where the lengths of the middle and largest sides are coprime.
2
12, 16, 18, 30, 32, 36, 40, 42, 44, 48, 50, 54, 56, 60, 64, 68, 70, 72, 76, 78, 80, 84, 90, 96, 98, 100, 104, 108, 110, 112, 114, 120, 126, 128, 130, 132, 136, 140, 144, 150, 152, 154, 156, 160, 162, 164, 168, 170, 172, 176, 180, 182, 186, 190, 192, 196, 198, 200, 204, 208
OFFSET
1,1
COMMENTS
This sequence includes the perimeters of all primitive Heronian triangles (A096468). First differs from A096468 at a(16) = 68.
LINKS
Eric Weisstein's World of Mathematics, Heronian Triangle
Wikipedia, Integer Triangle
EXAMPLE
a(1) = 12; there is one Heronian triangle with perimeter 12, which is [3,4,5] and the lengths of the middle and largest sides are coprime (GCD(4,5) = 1).
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).
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, May 18 2020
STATUS
approved