We present the detection of CO(5-4) with S/N> 7 - 13 and a lower CO transition with S/N > 3 (CO(4-3) for 4 galaxies, and CO(3-2) for one) with ALMA in band 3 and 4 in five main sequence star-forming galaxies with stellar masses 3-6x10^10 M/M_sun at 3 < z < 3.5. We find a good correlation between the total far-infrared luminosity LFIR and the luminosity of the CO(5-4) transition LCO(5-4), where LCO(5-4) increases with SFR, indicating that CO(5-4) is a good tracer of the obscured SFR in these galaxies. The two galaxies that lie closer to the star-forming main sequence have CO SLED slopes that are comparable to other star-forming populations, such as local SMGs and BzK star-forming galaxies; the three objects with higher specific star formation rates (sSFR) have far steeper CO SLEDs, which possibly indicates a more concentrated episode of star formation. By exploiting the CO SLED slopes to extrapolate the luminosity of the CO(1-0) transition, and using a classical conversion factor for main sequence galaxies of alpha_CO = 3.8 M_sun(K km s^-1 pc^-2)^-1, we find that these galaxies are very gas rich, with molecular gas fractions between 60 and 80%, and quite long depletion times, between 0.2 and 1 Gyr. Finally, we obtain dynamical masses that are comparable with the sum of stellar and gas mass (at least for four out of five galaxies), allowing us to put a first constraint on the alpha_CO parameter for main sequence galaxies at an unprecedented redshift.
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