On the number of partitions of a number into distinct divisors

Noah Lebowitz-Lockard and Joseph Vandehey
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 3, Pages 654–661
DOI: 10.7546/nntdm.2024.30.3.654-661
Full paper (PDF, 204 Kb)

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Authors and affiliations

Noah Lebowitz-Lockard
8330 Millman St., Philadelphia, PA, 19118, USA

Joseph Vandehey
Department of Mathematics, University of Texas at Tyler
3900 University Blvd., Tyler, TX, 75799, USA

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.

Keywords

  • Partitions
  • Distinct divisors
  • Asymptotics

2020 Mathematics Subject Classification

  • 11N37
    11P70

References

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Manuscript history

  • Received: 21 February 2024
  • Revised: 19 October 2024
  • Accepted: 25 October 2024
  • Online First: 31 October 2024

Copyright information

Ⓒ 2024 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Cite this paper

Lebowitz-Lockard, N., & Vandehey, J. (2024). On the number of partitions of a number into distinct divisors. Notes on Number Theory and Discrete Mathematics, 30(3), 654-661, DOI: 10.7546/nntdm.2024.30.3.654-661

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