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arXiv · 2510.03672

The Vandermonde Determinant of the Divisors of an Integer

Patrick Letendre
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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 $$ V(n) := \prod_{1 \le i < j \le \tau(n)}(d_{j}-d_{i}) \quad (n \ge 1). $$

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Patrick Letendre. 2025-10-04. The Vandermonde Determinant of the Divisors of an Integer. https://arxiv.org/abs/2510.03672

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