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Number of primitive triangles with integer sides a<=b<=c and inradius n; primitive means gcd(a, b, c) = 1.
2

%I #8 Jul 08 2013 18:36:25

%S 1,4,10,11,13,28,17,26,31,31,20,77,28,46,67,40,28,100,26,72,120,62,32,

%T 139,44,53,71,118,32,202,35,70,135,73,97,211,33,80,130,134,36,284,45,

%U 141,183,78,50,226,68,112,150,146,38,173,150,219,182,80,38,468,36,82

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

%D 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.

%H David W. Wilson, <a href="/A120261/b120261.txt">Table of n, a(n) for n = 1..10000</a>

%e a(3)=10 because 10 triangles have coprime integer sides and inradius 3, namely (7,24,25) (7,65,68) (8,15,17) (11,13,20) (12,55,65) (13,40,51) (15,28,41) (16,25,39) (19,20,37) (11,100,109).

%Y Cf. A120062, A120252.

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

%K nonn

%O 1,2

%A _David W. Wilson_, Jun 13 2006