A gozinta chain for $n$ is a sequence $\{1,a,b,\dots ,n\}$ where each element properly divides the next.
There are eight gozinta chains for $12$:
$\{1,12\}$, $\{1,2,12\}$, $\{1,2,4,12\}$, $\{1,2,6,12\}$, $\{1,3,12\}$, $\{1,3,6,12\}$, $\{1,4,12\}$ and $\{1,6,12\}$.
Let $g(n)$ be the number of gozinta chains for $n$, so $g(12)=8$.
$g(48)=48$ and $g(120)=132$.

Find the sum of the numbers $n$ not exceeding ${10}^{16}$ for which $g(n)=n$.