## Super Factorialicity

Check this out:
$66=2\times3\times11$

but $2+3+11=16$
Here is the interesting part:
$n=16$ is the largest value of $n$ such that $16^n$ divides $66!$ ($66!$ is read “sixty six factorial” and it is defined to be $66\times65\times64\times63\times\cdots\times3\times2\times1)$

Also:
$78=2\times3\times13$
$2+3+13=18$ and $18^{18}$ is the highest power of $18$ dividing $78!$.

Can you find any other examples of this phenomenon?

UPDATE!

I found another
$129=7\times47$
$7+47=54$ and
$54^{54}$ is the greatest power of $54$ that divides $129!$.