  Much progress has been made on the problem of calculating $g(n)$ for various
classes of integers $n$, where $g$ is the group-counting function. We approach
the inverse problem of solving the equations $g(n) = 6$ and $g(n) = 7$ in $n$.
The determination of $n$ for which $g(n) = k$ has been carried out by G. A.
Miller for $1 \le k \le 5$.
