Abstract: The ratios of the Bc(2S)+ to B+c, B?c(2S)+ to B+c, and B?c(2S)+ to Bc(2S)+ production cross sections are measured in proton-proton collisions at ?s=13??TeV, using a data sample collected by the CMS experiment at the LHC, corresponding to an integrated luminosity of 143??fb?1. The three measurements are made in the B+c meson phase space region defined by the transverse momentum pT>15??GeV and absolute rapidity |y|<2.4, with the excited B(*)c(2S)+ states reconstructed through the B(*)+c?+??, followed by the B+c?J/??+ and J/???+?? decays. The Bc(2S)+ to B+c, B?c(2S)+ to B+c, and B?c(2S)+ to Bc(2S)+ cross section ratios, including the unknown B(*)c(2S)+?B(*)+c?+?? branching fractions, are (3.47±0.63(stat)±0.33(syst))%, (4.69±0.71(stat)±0.56(syst))%, and 1.35±0.32(stat)±0.09(syst), respectively. None of these ratios shows a significant dependence on the pT or |y| of the B+c meson. The normalized dipion invariant mass distributions from the decays B(*)c(2S)+?B(*)+c?+?? are also reported.

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