The losses of runaway electrons due to magnetic perturbation fields are measured applying a scintillator probe during the flat top phases of purely ohmically heated low density discharges. The effects of well-defined amplitudes of the perturbation on the temporal evolution of the runaway losses and the spectral properties of the runaways are analyzed. The runaway transport towards the plasma edge is described by a model which takes magnetic turbulences and the magnetic perturbation field into account. Using an asymptotic theory, the orbits as well as radially and energy dependent transport coefficients for the runaways are calculated. A diffusion equation, which utilizes the coefficients, is solved delivering the density and the flux of the runaways. The model reproduces the measured enhancement of the runaway losses. Qualitatively different runaway spectra are found inside the plasma and at the edge. The spectra are explained by estimations of the competition between the secondary generation rate of the runaways and their radial diffusion. Thus, a self-consistent understanding of the temporal and spectral properties of the RE transport due to the resonant magnetic perturbation is achieved.