I want to know more about behavior of both Gamma function and zeta function writing them as a power in the form of harmonic series which i got the below form $$\sum_{n\geq 2}\dfrac1n\left(\Gamma\left(\frac1n\right)^{\zeta{\left(\frac1n\right)}}\right)$$ which seems converge as shown by Wolfram alpha it's seems converge approximately to $1.6$ But no way to get it's closed form since it's complicated , Now i want the exact value of that sum and it's closed value form if it exists however my narrow idea and attempts are fail to get it .
Note: The Motivation of this question is to know bounds of gamma function power zeta function for $n$ large enough