Let $d(n):=\sum _{d|n} 1$ be the number-of-divisors function. Wikipedia (here) defines the limit superior of $d(n)$ by
$$\underset{n\to \infty }{\overline{\text{lim}}}\frac{\log (d(n))}{\log (n)/\log (\log (n)) }=\log(2)$$
Rearranging terms gives
$$\underset{n\to \infty }{\overline{\text{lim}}}\log (d(n))=\frac{\log (2) \log (n)}{\log (\log (n))}$$
$$\underset{n\to \infty }{\overline{\text{lim}}}d(n)=e^{\frac{\log (2) \log (n)}{\log (\log (n))}}$$
But plotting $d[(n)$ and $e^{\frac{\log (2) \log (n)}{\log (\log (n))}}$ out to $n=10,000,000$ shows little sign of the suprema converging on this limit superior - perhaps due to the small size of $n$?
Can someone confirm that the $\underset{n\to \infty }{\overline{\text{lim}}}d(n)$ given above is correct, and either show how it is derived or point me to a source?