For a complex number $z$, given a function $f(z)=\sum_{i=1}^{n}\frac{1}{i^{z}}$.

Let $p_{j}$ be the j-th prime number $g(z) = \prod_{j=1}^{m}(1-p_{j}^{-z})$

Let $x = \lim_{n, m\rightarrow \infty} f(z)*g(z)$

Find the value of $\sum_{i=1, gcd(i, k) = x}^{i=k}1$ ,where $k = 354216846978542365$.