The minimal number with a given number of divisors Original Research Article

A number n is said to be ordinary if the smallest number with exactly n divisors is image where q1cdots, three dots, centeredqa is the prime factorization of n and q1greater-or-equal, slantedcdots, three dots, centeredgreater-or-equal, slantedqa (and where pk denotes the kth prime). We show here that all square-free numbers are ordinary and that the set of ordinary numbers has natural density one.