A120252 Number of primitive triangles with integer sides a<=b<=c and inradius n; primitive means gcd(a, b, c, n) = 1.

1, 4, 12, 13, 14, 28, 23, 27, 38, 33, 25, 81, 30, 52, 83, 44, 32, 101, 33, 80, 149, 73, 41, 146, 50, 61, 89, 132, 35, 204, 45, 80, 173, 79, 135, 220, 37, 85, 167, 156, 43, 291, 59, 164, 234, 88, 63, 236, 92, 126, 185, 162, 46, 179, 189, 258, 230, 94, 53, 483, 43, 94

Offset: 1

Author

Graeme McRae, Jun 12 2006

Keywords

• nonn

Comments

A120062(n) = sum_{k:k|n} a(k)

Examples

			a(3)= 12 because there are 12 primitive triangles with integer sides and inradius r=3. They are (10,10,12), (8,15,17), (11,13,20), (7,24,25), (8,26,30), (19,20,37), (16,25,39), (15,28,41), (13,40,51), (12,55,65), (7,65,68), (11,100,109).
		

References

• Mohammad K. Azarian, Circumradius and Inradius, Problem S125, Math Horizons, Vol. 15, Issue 4, April 2008, p. 32. Solution published in Vol. 16, Issue 2, November 2008, p. 32.

Links

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

Crossrefs

Cf. A120062.

See A120062 for sequences related to integer-sided triangles with integer inradius n.

Formula

Moebius transform of A120062. - David W. Wilson, Jun 14 2006