On the maximal order of numbers in the "factorisatio numerorum" problem

Martin Klazar, Florian Luca

Let m(n) be the number of ordered factorizations of n in factors larger than 1. We prove that for every eps>0 n^{rho} m(n) < exp[(log n)^{1/rho}/(loglog n)^{1+eps}] holds for all i…