  In this document will be proved a formula to compute the $p$-adic valuation
of a hyperfactorial. We call a hyperfactorial the result of multiplying a given
number of consecutive integers from 1 to the given number,each raised to its
own power. For example, the hyperfactorial of $n$ is equal to: $1^1 2^2
3^3\dots n^n$ . Lots of studies have been done about the hyperfactorial
function, in particular two mathematicians: Glaisher and Kinkelin, who have
found the asymptotic behaviour of this function as $n$ that approaches infinity
(finding a costant, the Glaisher-Kinkelin costant, which has a lot of
expressions using the Euler Gamma function and the Riemann Zeta function). In
particular in this document I'll write about the p-adic valuation of this
function, or rather the maximum exponent of $p$($p$ a prime integer) such that
$p$ raised to that power divides the hyperfactorial of $n$. The formula which I
will present uses the famous De-Polignac formula for the $p$-adic valuation of
the simple factorial. Then I'll discuss about the asymptotic analysis of our
result.
