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The weak-coupling expansion of the QCD pressure is known up to the order g6 log g. However, at experimentally relevant temperatures, the corresponding series is poorly convergent. In this proceedings, we discuss at which extent the gauge-invariant resummation scheme, Hard-Thermal-Loop perturbation theory (HTLpt), improves the apparent convergence. We first present HTLpt results for QCD thermodynamic functions up to three-loop order at vanishing chemical potential. Then, we report a preliminary HTLpt result of one-loop quark number susceptibility, probing the finite density equation of state. Our results are consistent with lattice data down to 2 − 3Tc, reinforcing the weakly-coupled quasiparticle picture in the intermediate coupling regime

Hard-Thermal-Loop QCD thermodynamics and quark number susceptibility