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Using e + e − collision data corresponding to a total integrated luminosity of 20 fb − 1 collected with the BESIII detector at the BEPCII collider, we present a measurement of the Born cross section for the process at 39 center-of-mass energies between 3.5 and 4.9 GeV with a partial reconstruction technique. By performing a fit to the dressed cross section of with a power law function for continuum production and one resonance at a time for the ψ (3770), ψ (4040), ψ (4160), ψ (4230), ψ (4360), ψ (4415) or ψ (4660), respectively, the upper limits for the product of partial electronic width and branching fraction into the final state for these resonances are determined at the 90% confidence level.