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Direct numerical simulations of hydrodynamical turbulence are performed in the presence of a large-scale forcing up to Taylor-based Reynolds numbers of 800 for a Taylor-Green flow and 1000 for ABC forcing. Statistics on the triadic interactions responsible for the transfer of energy, and on their integrated counterparts are obtained from simulations with a turbulent steady state integrated for more than ten eddy turn-over times. The maximum resolution of the runs performed on regular grids are 10243 points. It is shown that the energy transfer is local but at the highest resolution as much as 20% of it comes from non-local interactions involving widely separated scales, with a particular emphasis on the forcing scale k0/-1. The scaling of the ratio of nonlocal to local energy flux with Reynolds number is found to be a power law. [ABSTRACT FROM AUTHOR]