The Ramanujan Journal

, Volume 49, Issue 1, pp 87–96 | Cite as

The partition function p(n) in terms of the classical Möbius function

  • Mircea MercaEmail author
  • Maxie D. Schmidt


In this paper, we investigate decompositions of the partition function p(n) from the additive theory of partitions considering the famous Möbius function \(\mu (n)\) from multiplicative number theory. Some combinatorial interpretations are given in this context. Our work extends several analogous identities proved recently relating p(n) and Euler’s totient function \(\varphi (n)\).


Lambert series Möbius function q-series partition function 

Mathematics Subject Classification

11A25 11P81 05A17 05A19 



The authors thank the referees for their helpful comments.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Academy of Romanian ScientistsBucharestRomania
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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