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We report on the inclusive J/ψ production cross section measured at the CERN Large Hadron Collider in proton-proton collisions at a centre-of-mass energy s√ = 13 TeV. The J/ψ mesons are reconstructed in the e+e− decay channel and the measurements are performed at midrapidity (|y|<0.9) in the transverse-momentum interval 0<pT<40 GeV/c, using a minimum bias data sample corresponding to an integrated luminosity Lint=32.2 nb−1 and an Electromagnetic Calorimeter triggered data sample with Lint=8.3 pb−1. The pT-integrated J/ψ production cross section at midrapidity, computed using the minimum bias data sample, is dσ/dy|y=0=8.97±0.24 (stat)±0.48 (syst)±0.15 (lumi) μb. An approximate logarithmic dependence with the collision energy is suggested by these results and available world data, in agreement with model predictions. The integrated and pT-differential measurements are compared with measurements in pp collisions at lower energies and with several recent phenomenological calculations based on the non-relativistic QCD and Color Evaporation models.