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

1,2

Comments

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

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

Formula

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

Example

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).

Crossrefs

Cf. A120062.

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

Sequence in context: A009115 A051434 A074138 * A103053 A087760 A237279

Adjacent sequences: A120249 A120250 A120251 * A120253 A120254 A120255

Keyword

nonn

Author

Graeme McRae, Jun 12 2006

Status

approved