  We calculate F^4 and R^4T^(4g-4) couplings in d=8 heterotic and type I string
vacua (with gauge and graviphoton field strengths F,T, and Riemann curvature
R). The holomorphic piece F_g of the heterotic one-loop coupling R^4T^(4g-4) is
given by a polylogarithm of index 5-4g and encodes the counting of genus g
curves with g nodes on the K3 of the dual F-theory side. We present closed
expressions for world-sheet tau-integrals with an arbitrary number of lattice
vector insertions. Furthermore we verify that the corresponding heterotic
one-loop couplings sum up perturbative open string and non-perturbative
D-string contributions on the type I side. Finally we discuss a type I one-loop
correction to the R^2 term.
