We examine the dependence on main shock magnitudemof thepandχparameters appearing in Omori‐Utsu formulaλ(t,m) =χ× (t+c)−prelating the rate of aftershocksλat timetafter a main shock. Observations point out to a significant increase ofpwithm, along with a scaling relationship of the formχ∼ 10αm. 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 atm= 2). Finally, the influence of afterslip on parameterspandχis studied to highlight the fact that it can significantly perturb thep(m) andχ(m) relations obtained with the initial afterslip‐free model.