A309312 Areas of Heronian triangles that uniquely define the lengths of the triangle's sides.

6, 30, 42, 54, 66, 72, 114, 132, 150, 198, 204, 234, 294, 306, 378, 390, 408, 468, 486, 522, 570, 594, 648, 684, 726, 744, 750, 798, 816, 876, 984, 1014, 1026, 1110, 1170, 1218, 1254, 1290, 1332, 1350, 1368, 1428, 1494, 1518, 1548, 1554, 1590, 1734, 1770, 1782, 1806, 1938, 1950, 1974

Offset: 1

Author

Jacob Vecht, Jul 22 2019

Keywords

• nonn
• easy

Comments

These are not necessarily primitive Heronian triangles. The corresponding sequence for primitive Heronian triangles is neither a subset nor a superset of this sequence.

Examples

			A triangle with integer sides and an area of 42 square units necessarily has sides 7,15,20, so 42 is a term. 12 is not a term because an area of 12 could have sides 6,5,5 or 8,5,5.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 500 terms from Jacob Vecht)
• Wikipedia, Heronian triangle

Crossrefs

Subsequence of A188158.

Extensions

Corrected 37th term "1248" to "1254".