Although cuprate high-temperature superconductors were discovered already in 1986 the origin of the pairing mechanism remains elusive. While the doped compounds are superconducting with high transition temperatures T-c, the undoped compounds are insulating due to the strong effective Coulomb interaction between the Cu 3d holes. We investigate the dependence of the maximum superconducting transition temperature T-cmax on the on-site effective Coulomb interaction U using the constrained random-phase approximation. We focus on the commonly used one-band model of the cuprates, including only the antibonding combination of the Cu d(x2-y2) and O p(x) and p(y) orbitals and find a screening-dependent trend between the static value of U and T-cmax for the parent compounds of a large number of hole-doped cuprates. Our results suggest that superconductivity may be favored by a large on-site Coulomb repulsion. We analyze both the trend in the static value of U and its frequency dependence in detail and, by comparing our results to other works, speculate on the mechanisms behind the trend.