  In this article we present the worldsheet integrand for one-loop amplitudes
in maximally supersymmetric superstring theory involving any number n of
massless open string states. The polarization dependence is organized into the
same BRST invariant kinematic combinations which also govern the leading string
correction to tree level amplitudes. The dimensions of the bases for both the
kinematics and the associated worldsheet integrals is found to be the unsigned
Stirling number S_3^{n-1} of first kind. We explain why the same combinatorial
structures govern on the one hand finite one-loop amplitudes of equal helicity
states in pure Yang Mills theory and on the other hand the color tensors at
quadratic alpha prime order of the color dressed tree amplitude.
