A Partition Identity Related to Stanley's Theorem - Merca, Mircea; Schmidt, Maxie D (arXiv.org, 2023)
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.