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arXiv · 2310.13672

A Partition Identity Related to Stanley's Theorem

Mircea Merca·Maxie D. Schmidt
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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.

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Mircea Merca, Maxie D. Schmidt. 2023-10-20. A Partition Identity Related to Stanley's Theorem. https://doi.org/10.1080/00029890.2018.1521232

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