  We take an approach toward counting the number of n for which the curves E_n:
y^2=x^3-n^2x have 2-Selmer groups of a given size. This question was also
discussed in a pair of Invent. Math. papers by Roger Heath-Brown. We discuss
the connection between computing the size of these Selmer groups and verifying
cases of the Birch and Swinnerton-Dyer Conjecture. The key ingredient for the
asymptotic formulae is the ``independence'' of the Legendre symbol evaluated at
the prime divisors of an integer with exactly k prime factors.
