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In view of the good agreement between the LHCb prompt-ηc data at s=7 and 8 TeV and the NLO colour-singlet model predictions –i.e. the leading v2 NRQCD contribution–, we provide predictions in the LHCb acceptance for the forthcoming 13 TeV analysis bearing on data taken during the LHC Run2. We also provide predictions for s=115 GeV for proton-hydrogen collisions in the fixed-target mode which could be studied during the LHC Run3. Our predictions are complemented by a full theoretical uncertainty analysis. In addition to cross section predictions, we elaborate on the uncertainties on the pp¯ branching ratio –necessary for data-theory comparison– and discuss other usable branching fractions for future studies.