A Partition Identity Related to Stanley's Theorem

Abstract

In this paper, we use the Lambert series generating function for Euler's totient function to introduce a new identity for the number of $1$'s in the partitions of $n$. A new expansion for Euler's partition function $p(n)$ is derived in this context. These surprising new results connect the famous classical totient function from multiplicative number theory to the additive theory of partitions.

Preprint version of the article submitted for publication in 2017

Cited by in corpus (2)

• The partition function $p(n)$ in terms of the classical Möbius function
• Overpartitions and functions from multiplicative number theory