On the number of abelian groups of a given order and the number of prime factors of an integer


Aleksandar Ivić




Let $a(n)$ and $u(n)$ denote the number of non-isomorphic Abelian groups with $n$ elements and the number of distinct prime factors of $n$ respectively. The distribution of values of $a(n)$ (which is multiplicative) and $\omega(n)$ (which is additive) is compared in several ways.