In 1966, Shanks and Schmid investigated the asymptotic behavior of the number
of positive integers less than or equal to x which are represented by the
quadratic form X^2+nY^2, n greater than or equal to 1. Based on some numerical
computations, they observed that the constant occurring in the main term
appears to be the largest for n=2. In this paper, we prove that in fact this
constant is unbounded as one runs through fundamental discriminants with a
fixed number of distinct prime divisors.