|
%I #15 Aug 18 2017 14:31:21
%S 1,1,2,1,2,2,2,2,2,2,3,2,2,3,4,2,3,2,3,3,4,2,4,4,2,4,3,2,4,4,4,3,4,3,
%T 6,3,2,4,6,4,5,4,3,4,4,3,6,4,3,4,6,3,4,4,6,6,4,2,7,4,4,5,6,3,6,6,3,5,
%U 6,4,8,4,3,6,6,4,6,4,6,6,4,3,7,6,4,6,8,4,7,6,6,4,4,5,10,6,3,5,6,3
%N Number of unordered primitive solutions to xy+xz+yz=n.
%C For n = m^2 this is the number of root Descartes quadruples (-m,b,c,d).
%C An upper bound on the number of solutions appears to be 1.5*sqrt(n). - _T. D. Noe_, Jun 14 2006
%H T. D. Noe, <a href="/A067754/b067754.txt">Table of n, a(n) for n = 1..10000</a>
%H R. L. Graham, J. C. Lagarias, C. L. Mallows, Allan Wilks, and C. H. Yan, <a href="http://arxiv.org/abs/math/0009113">Apollonian Circle Packings: Number Theory</a>, J. Number Theory, 100 (2003), 1-45.
%F a(n) = A066360(n) + A007875(n). - _T. D. Noe_, Jun 14 2006
%e a(9)=2 because of (0,1,9) and (1,1,4) (but not (0,3,3)).
%t Table[cnt=0; Do[z=(n-x*y)/(x+y); If[IntegerQ[z] && GCD[x,y,z]==1, cnt++ ], {x,0,Sqrt[n/3]}, {y, Max[1,x],Sqrt[x^2+n]-x}]; cnt, {n,100}] (* _T. D. Noe_, Jun 14 2006 *)
%Y Cf. A067751, A067752, A067753.
%K easy,nonn
%O 1,3
%A _Colin Mallows_, Jan 31 2002
%E Corrected and extended by _T. D. Noe_, Jun 14 2006
|
