A strong effect of the third moment of the molecular weight distribution on the melt linear viscoelastic response of linear polyethylene samples is reported. The Newtonian viscosity of samples with broad molecular weight distributions shows a noticeable increase with respect to model linear samples with the same weight-average molecular weight but symmetric and narrower molecular weight distributions. These experimental results are in agreement with previous empirical and theoretical studies based on reptation concepts that predict a dependence of the viscosity in terms of the M-z/M-w ratio. In addition, it is possible to obtain a description of the whole linear viscoelastic fingerprint of the samples by mapping the entanglement parameters obtained from atomistic simulations together with the molecular features into the reptation model. The results shown here are of great importance, as the Newtonian viscosity-molecular weight relationship has become a widely used tool, not only to test the molecular weight dependence, but also to assess the possible presence of long-chain branching in polyolefins.