Distribution of the Number of Factors in Random Ordered Factorizations of Integers, Original Research Article

We study in detail the asymptotic behavior of the number of ordered factorizations with a given number of factors. Asymptotic formulae are derived for almost all possible values of interest. In particular, the distribution of the number of factors is asymptotically normal. Also we improve the error term in Kalmárʹs problem of “factorisatio numerorum” and investigate the average number of district factors in a random ordered factorization.