On the number of partitions of a number into distinct divisors

Abstract

Let $p_{\textrm{dsd}} (n)$ be the number of partitions of $n$ into distinct squarefree divisors of $n$. In this note, we find a lower bound for $p_{\textrm{dsd}} (n)$, as well as a sequence of $n$ for which $p_{\textrm{dsd}} (n)$ is unusually large.

Theorems & Definitions (14)

• Theorem 1
• Theorem 2: BEO
• Theorem 3
• Theorem 4
• Theorem 5
• Lemma 6
• proof
• proof : Proof of Theorem \ref{['main thm']}
• Lemma 7
• proof