[math-fun] Numbers of the form K^2 + KL + L^2

Numbers of the form K^2 + KL +L^2, K and L integers, arise often when making calculations connected with the triangular lattice in the plane. Let tau = exp(2pi*i/6). For K, L > 0, K^2 + KL +L^2 is, among other things, the number of points in the quotient ring Z{tau] / <K + L*tau> namely, the Eisenstein integers factored out by its ideal <K + L*tau>. I would like to know more about these numbers. For example: * Given any integer N, is there a simple test for whether N is of the form K^2 + KL + L^2 for some integers K, L ??? * What can be said about the prime factorization of K^2 + KL + L^2 ??? * Is there a relationship of such numbers to Eisenstein primes? —Dan