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A335150 Perimeters of Heronian triangles whose smallest side length is coprime to their middle side and whose middle side length divides their perimeter. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A109275 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

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Last modified May 17 08:05 EDT 2022. Contains 353741 sequences. (Running on oeis4.)