A120252 - OEIS

%I #10 Jul 08 2013 13:37:14

%S 1,4,12,13,14,28,23,27,38,33,25,81,30,52,83,44,32,101,33,80,149,73,41,

%T 146,50,61,89,132,35,204,45,80,173,79,135,220,37,85,167,156,43,291,59,

%U 164,234,88,63,236,92,126,185,162,46,179,189,258,230,94,53,483,43,94

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

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

%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="/A120252/b120252.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HeronianTriangle.html">Heronian Triangle</a>

%F Moebius transform of A120062. - _David W. Wilson_, Jun 14 2006

%e 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).

%Y Cf. A120062.

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

%K nonn

%O 1,2

%A _Graeme McRae_, Jun 12 2006