Is $coNP^{\#P}=NP^{\#P}=P^{\#P}$?
It is an open problem in complexity theory for many years if $\mathsf{PH}^{\mathsf{\#P}}$ collapse,
where $\mathsf{PH}$ is the polynomial time hierarchy. It is also an open problem to construct
an oracle to separate $\mathsf{P}^{\mathsf{\#P}}$ from $\mathsf{PSPACE}$.