A239246 Number of primitive Heronian triangles with n as greatest side length.

0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 2, 0, 3, 0, 0, 2, 2, 0, 0, 1, 3, 2, 0, 1, 2, 3, 0, 0, 0, 0, 2, 1, 5, 0, 4, 3, 4, 1, 0, 2, 1, 0, 0, 2, 0, 2, 4, 6, 4, 0, 2, 2, 0, 2, 0, 1, 3, 0, 1, 0, 8, 2, 0, 5, 1, 2, 0, 0, 6, 2, 7, 0, 3, 0, 0, 3, 0, 2, 0, 0, 9

Offset: 1

Author

Frank M Jackson, Mar 13 2014

Keywords

• nonn

Examples

			a(17)=3 as there are 3 primitive Heronian triangles with greatest side length of 17. They are (9, 10, 17), (8, 15, 17) and (16, 17, 17).
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Heronian Triangle.

Crossrefs

Cf. A054875, A070138, A096467, A123323, A134587.

Programs

Mathematica

nn=200; lst={}; Do[s=(a+b+c)/2; If[IntegerQ[s]&&GCD[a, b, c]==1, area2=s(s-a)(s-b)(s-c); If[area2>0&&IntegerQ[Sqrt[area2]], AppendTo[lst, c]]], {c, 3, nn}, {b, c}, {a, b}]; Table[Length@Select[lst, #==n &], {n, 1, nn}] (* using T. D. Noe's program at A083875 *)