On the number of partitions of a number into distinct divisors

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.

Authors

Publication Details

Journal
Notes on Number Theory and Discrete Mathematics
Published
2024-10-31
DOI
https://doi.org/10.7546/nntdm.2024.30.3.654-661
Primary Topic
Advanced Mathematical Identities
Type
article
Field-Weighted Citation Impact
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article

On the number of partitions of a number into distinct divisors

Noah Lebowitz-Lockard, Joseph Vandehey
Notes on Number Theory and Discrete Mathematics
Advanced Mathematical Identities
article

On the number of partitions of a number into distinct divisors

Noah Lebowitz-Lockard, Joseph Vandehey
article en

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.

Notes on Number Theory and Discrete MathematicsVol. 30(3)
Openalex Percentile: Top 65%
Advanced Mathematical Identities
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