  In equilibrium, colloidal suspensions governed by short-range attractive and
long-range repulsive interactions form thermodynamically stable clusters. Using
Brownian dynamics computer simulations, we investigate how this equilibrium
clustering is affected when such particles are self-propelled. We find that the
clustering process is stable under self-propulsion. For the range of
interaction parameters studied and at low particle density, the cluster size
increases with the speed of self-propulsion (activity) and for higher activity
the cluster size decreases, showing a non-monotonic variation of cluster size
with activity. This clustering behaviour is distinct from the pure kinetic (or
motility-induced) clustering of self-propelling particles which is observed at
significantly higher activities and densities. We present an equilibrium model
incorporating the effect of activity as activity-induced attraction and
repulsion by imposing that the strength of these interactions depend on
activity superlinearly. The model explains the cluster size dependence of
activity obtained from simulations semi-quantitatively. Our predictions are
verifiable in experiments on interacting synthetic colloidal microswimmers
