The modular Erdős–Burgess constant conjecture

Let $n>1$ be an integer, and let $R=\mathbb{Z}_n$ be the ring of integers modulo $n$. The modular Erdős–Burgess constant conjecture.

$${\rm I}(\mathcal{S}_R)={\rm D}(R^{\times})+\Omega(n)-\omega(n).$$

This conjecture gives an exact formula for the Erdős–Burgess constant of the multiplicative semigroup of $R$. The formula is proved in the paper when $n$ is a prime power or a product of distinct primes, but remains open for general $n$.