We present a study of the effects of strong correlations in rare-earth pnictides, in which localized 4f states simultaneously retain atomiclike character and strongly influence the free-electron-like valence electron states. Using erbium arsenide as our example, we use a modern implementation of dynamical mean-field theory to obtain the atomic multiplet structure of the Er3+ 4f shell, as well as its unusually strong coupling to the electronic Fermi surfaces; these types of behavior are not correctly described within conventional electronic-structure methods. We are then able to explain the long-standing theoretical question of the quasisaturation of magnetization in an applied magnetic field, and to obtain the first quantitative agreement with experimental Shubnikov-de Haas frequencies of the Fermi-surface sheets.