We present the equation of state for a coarse-grained model of polymer melts where each chain is represented as a soft colloidal particle centered on its center-of-mass. The formalism is based on the solution of the Ornstein-Zernike equation and is analytical, allowing for the formal investigation of the elements that ensure thermodynamic consistency in coarse-grained models of polymer melts. By comparing predictions from our expressions with those from computer simulations of the coarse-grained system and with atomistic polymer integral equation theory, we demonstrate that both structural and thermodynamic consistency with the atomistic level description is maintained during our coarse-graining procedures.