A335150 Perimeters of Heronian triangles whose smallest side length is coprime to their middle side and whose middle side length divides their perimeter.

12, 42, 78, 84, 114, 156, 186, 222, 228, 258, 294, 366, 372, 402, 438, 444, 474, 516, 546, 582, 588, 618, 654, 732, 762, 798, 804, 834, 876, 906, 942, 948, 978, 1014, 1086, 1092, 1158, 1164, 1194, 1236, 1266, 1302, 1308, 1338, 1374, 1446, 1482, 1524, 1554, 1596

Offset

1,1

Comments

Among the 42352 terms below 2*10^6 we observe that if multiples triangles correspond to a term their middle sides coincide. In this range there are perimeters common to 1, 2, 4, 8, and 16 triangles. The first such terms are a(1) = 12, a(4) = 84, a(36) = 1092, a(546) = 20748, a(14273) = 643188, and the corresponding middle sides are 4, 28, 364, 6916, and 214396. - Giovanni Resta, May 30 2020

Links

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

Eric Weisstein's World of Mathematics, Heronian Triangle

Wikipedia, Heronian triangle

Wikipedia, Integer Triangle

Crossrefs

Cf. A335149.

Sequence in context: A360961 A241854 A085798 * A270700 A282693 A045945

Adjacent sequences: A335147 A335148 A335149 * A335151 A335152 A335153

Keyword

nonn

Author

Wesley Ivan Hurt, May 25 2020

Extensions

Terms a(27) and beyond from Giovanni Resta, May 30 2020

Status

approved