Conjecture: \begin{align} \lim_{n\to \infty } \, \frac{\left(\prod _{k=1}^n \phi (k)\right){}^{1/n}}{n}\sim 0.2059\text{...} \end{align}

The numerical result from 100000 terms is:

My questions are:

1) exists this limit ?

2) if yes, what is closed form of this constant ?

I am sure that this limit is NOT equal to 6/Pi^2 * exp(-1) = 0.2236438825...