Squarefree Hilbert number

In the multiplicative set of Hilbert numbers, a squarefree Hilbert number is one divisible by no square $h^2$ of a Hilbert number $h>1$. This is weaker than being a squarefree integer: $9$ is a squarefree Hilbert number because its square divisor $9=3^2$ has $3$ outside the Hilbert numbers.