This is joint work with Brandon Hanson.

Let H(Z) be the set of odd squarefree numbers not exceeding Z, let r(n,z) denote the number of solutions of x^2+zy^2=n in positive integers x,y, and let R(n;Z) be the sum of r(n;Z} over all z in H. Then we show that for any constant c, if Z=C(log X), then R(n;Z)>0 for >> X values of n<=Z.