We examine the dependence on main shock magnitude m of the p and χ parameters appearing in Omori-Utsu formula λ(t, m) = χ × (t + c)−p relating the rate of aftershocks λ at time t after a main shock. Observations point out to a significant increase of p with m, along with a scaling relationship of the form χ ∼ 10 α m . Here we show that these observations can be explained within the framework of the rate-and-state friction model when accounting for realistic levels of coseismic stress heterogeneity on the main fault. We constrain the model parameters in order to recover the trends observed in previous and new analyses of aftershock sequences. The expected ratio of the coseismic stress drop standard deviation to its mean is found to be of the order of a few units for large (m = 7) earthquakes, resulting in a very rough stress field at the small scale, while it is much smoother at small magnitudes (ratio ≃ 0.1 at m = 2). Finally, the influence of afterslip on parameters p and χ is studied to highlight the fact that it can significantly perturb the p(m) and χ(m) relations obtained with the initial afterslip-free model.