Recent results by the Planck collaboration have shown that cosmological parameters derived from the cosmic microwave background anisotropies and cluster number counts are in tension, with the latter preferring lower values of the matter density parameter, $Omega_mathrm{m}$, and power spectrum amplitude, $sigma_8$. Motivated by this, we investigate the extent to which the tension may be ameliorated once the effect of baryonic depletion on the cluster mass function is taken into account. We use the large-volume Millennium Gas simulations in our study, including one where the gas is pre-heated at high redshift and one where the gas is heated by stars and active galactic nuclei (in the latter, the self-gravity of the baryons and radiative cooling are omitted). In both cases, the cluster baryon fractions are in reasonably good agreement with the data at low redshift, showing significant depletion of baryons with respect to the cosmic mean. As a result, it is found that the cluster abundance in these simulations is around 15 per cent lower than the commonly-adopted fit to dark matter simulations by Tinker et al (2008) for the mass range $10^{14}-10^{14.5}h^{-1} mathrm{M}_odot$. Ignoring this effect produces a significant artificial shift in cosmological parameters which can be expressed as $Delta[sigma_8(Omega_mathrm{m}/0.27)^{0.38}]simeq -0.03$ at $z=0.17$ (the median redshift of the $mathit{Planck}$ cluster sample) for the feedback model. While this shift is not sufficient to fully explain the $mathit{Planck}$ discrepancy, it is clear that such an effect cannot be ignored in future precision measurements of cosmological parameters with clusters. Finally, we outline a simple, model-independent procedure that attempts to correct for the effect of baryonic depletion and show that it works if the baryon-dark matter back-reaction is negligible.
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