Product of Divisors of a Function

Can we find a simple expression for the divisors of a number? Yes we can. If  
\[d | n\]
  then  
\[d, \; \frac{n}{d}\]
  are both divisors of  
\[n\]
  and so  
\[\prod_{d | n} d= \prod_{d | n} \frac{n}{d}\]
. There are  
\[\tau (n)\]
  divisors of  
\[n\]
  so
\[\prod_{d | n} d \prod_{d | n} \frac{n}{d} = \prod_{d | n} d \frac{n}{d} = \frac{d | n} n= n^{\tau (n)} \]

where  
\[\tau (n)\]
  is Euler's Totient Function. Hence  
\[\prod_{d | n} d= n^{\frac{\tau (n)}{2}}\]
.

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