Étude statistique du facteur premier médian, 1 : valeur moyenne

We provide an asymptotic expansion for the mean-value of the logarithm of the middle prime factor of an integer, defined according to multiplicity or not, thus generalising a recent study of McNew, Pollack, and Singha Roy. This yields an improvement of the asymptotic estimate, in particular by furnishing an optimal remainder when the expansion is truncated at the first order.