  We give an exact formula for the number of normal subgroups of each finite
index in the Baumslag-Solitar group BS(p,q) when p and q are coprime. Unlike
the formula for all finite index subgroups, this one distinguishes different
Baumslag-Solitar groups and is not multiplicative. This allows us to give an
example of a finitely generated profinite group which is not virtually
pronilpotent but whose zeta function has an Euler product.
