Given Birkhoff’s pointwise ergodic theorem, it is natural to consider whether convergence still holds along subsequences of the integers. In this talk, we investigate convergence of ergodic averages along the number theoretic sequence $\mathrm{\Omega }(n)$, where $\mathrm{\Omega }(n)$ denotes the number of prime factors of $n$ counted with multiplicities. In particular, we demonstrate that, although a pointwise ergodic theorem does not hold along $\mathrm{\Omega }(n)$, there are multiple instances in which we can recover convergence. We also present a more general criterion for identifying slow-growing sequences possessing a certain divergence property exhibited by $\mathrm{\Omega }(n)$. This talk is based on joint work with Sovanlal Mondal (Ohio State).