A305704 Numbers that are the semiperimeter of some triangle with integer sides and area.

6, 8, 9, 12, 15, 16, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 48, 49, 50, 52, 54, 55, 56, 57, 60, 63, 64, 65, 66, 68, 70, 72, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 93, 95, 96, 98, 99, 100, 102, 104, 105

Offset: 1

Author

Peter Kagey, Jun 08 2018

Keywords

• nonn

Links

• Peter Kagey, Table of n, a(n) for n = 1..1000
• Eric Weisstein's World of Mathematics, Heronian Triangle

Crossrefs

Cf. A051518.

Programs

Mathematica

hp[p_] := Catch@ Block[{c, q=p/2}, Do[c = p-a-b; If[IntegerQ@ Sqrt[q (q-a) (q-b) (q-c)], Throw@ True], {a, p/2-1}, {b, p/2-a+1, p/2-1}]; False]; Select[Range@ 105, hp[2 #] &] (* Giovanni Resta, Jun 14 2018 *)

Formula

a(n) = A051518(n)/2.