The safety-factor profile of a magnetically diverted tokamak plasma diverges logarithmically as the magnetic separatrix (a.k.a. the last closed magnetic flux-surface) is approached. At first sight, this suggests that, when determining the response of such a plasma to a static, externally generated, resonant magnetic perturbation (RMP), it is necessary to include an infinite number of rational magnetic flux-surfaces (at which the RMP resonates with the equilibrium magnetic field) in the calculation, the majority of which lie very close to the separatrix. In fact, when finite plasma resistivity is taken into account, this turns out not to be the case. Instead, it is only necessary to include rational surfaces that lie in the region , where is the normalized poloidal magnetic flux, and . The parameter can be calculated from the edge plasma parameters.