Perfect-power conjecture for the plane partition function

Let $pl(n)$ denote the plane partition function, counting plane partitions of $n$. A perfect power is an integer of the form $a^b$ with integers $a,b>1$. The plane-partition perfect-power conjecture. The plane partition function $pl(n)$ is never a perfect power of the form $a^b$ for integers $a,b>1$. This is proposed as an analogue of Sun's conjecture for plane partitions and remains open in the source.