A formula for the normal subgroup growth of Baumslag-Solitar groups

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.