Earth's core is less dense than iron, and therefore it must contain "light elements," such as S, Si, O, or C. We use ab initio molecular dynamics to calculate the density and bulk sound velocity in liquid metal alloys at the pressure and temperature conditions of Earth's outer core. We compare the velocity and density for any composition in the (Fe-Ni, C, O, Si, S) system to radial seismological models and find a range of compositional models that fit the seismological data. We find no oxygen-free composition that fits the seismological data, and therefore our results indicate that oxygen is always required in the outer core. An oxygen-rich core is a strong indication of high-pressure and high-temperature conditions of core differentiation in a deep magma ocean with an FeO concentration (oxygen fugacity) higher than that of the present-day mantle.