Hao–Wang–Zhang equality conjecture for the Erdős–Burgess constant

For an integer $n>1$, let $I_r(\mathbb{Z}/n\mathbb{Z})$ denote the Erdős–Burgess constant of the multiplicative semigroup $\mathbb{Z}/n\mathbb{Z}$, let $\mathsf{D}(G)$ be the Davenport constant of a finite abelian group $G$, and let $\Omega(n)$ and $\omega(n)$ denote, respectively, the number of prime factors of $n$ counted with multiplicity and the number of distinct prime divisors of $n$. Hao–Wang–Zhang equality conjecture. For every integer $n>1$,

$$I_r(\mathbb{Z}/n\mathbb{Z})=\mathsf{D}((\mathbb{Z}/n\mathbb{Z})^{\times})+\Omega(n)-\omega(n).$$

The corresponding inequality is known, with equality when $n$ is a prime power or a product of distinct primes. The conjecture asks whether equality holds for all $n>1$, strengthening the known lower bound and relating the Erdős–Burgess and Davenport constants.