The Vandermonde Determinant of the Divisors of an Integer

Abstract

Let $1=d_1<d_2<\cdots <d_{\tau (n)}=n$ denote the ordered sequence of the positive divisors of an integer $n$. We are interested in estimating the arithmetic function $$V(n):=\prod _{1\le i<j\le \tau (n)}(d_j-d_i)(n\ge 1).$$