Molecular dynamics (MD) simulations of united atom models for alkane melts are compared with a recently developed theory for calculating the memory functions of flexible polymers. The theory is based upon an approximate solution of the diffusion equation without hydrodynamic interactions. The polymer dynamics are described by using time correlation functions which are expressed in terms of a set of equilibrium averages and the approximate eigenvalues and eigenfunctions of the diffusion operator. For flexible enough chains with sufficiently high molecular weight, the hydrodynamic interactions are screened, and the simplified solvent model used by the theory is expected to be adequate. The only parameter not defined by the MD simulations is the bead friction coefficient zeta. In the limit of weak hydrodynamic interactions (Rouse dynamics), zeta can be determined from the molecular diffusion coefficient by applying the Rouse relation D = kT/N zeta(R). Given this choice of zeta(R), the time correlation functions computed from the theory are compared with those obtained directly from the MD simulations. Excellent agreement with the simulations is found for all correlation functions and all times for the decane dynamics, provided the theory employs one scale factor to increase zeta(R) and, hence, to compensate for the inadequacy of the Rouse relation. The same picture holds for hexadecane and triacontane (C30H62) but With Smaller scale factors. Scaling becomes unnecessary for C44H90 which is long enough for the crossover to Rouse dynamics for D to be almost complete. Very good agreement (after appropriate scaling of zeta(R)) also emerges between theory and simulations for several branched alkanes with carbon numbers C-25-C-30. Computations for hexadecane at different temperatures show that the scale factors may be weakly temperature dependent.