The cross sections of the 70Ge(p,gamma)71As and 76Ge(p,n)76As reactions have been measured with the activation method in the Gamow window for the astrophysical p process. The experiments were carried out at the Van de Graaff and cyclotron accelerators of ATOMKI. The cross sections have been derived by measuring the decay gamma-radiation of the reaction products. The results are compared to the predictions of Hauser-Feshbach statistical model calculations using the code NON-SMOKER. Good agreement between theoretical and experimental S factors is found. Based on the new data, modifications of the optical potential used for low-energy protons are discussed.