Let $C(n)$ be $\sum (\phi(a) \times b)$ taken over ordered pairs $(a, b)$ of positive integers for which $a \times b$ divides $n$.

Let $F(k) = \sum_{i=1}^{k} \frac{C(i)}{i}$.

Let $x = \sum_{k=1}^{\infty} \frac{F(k)}{k \times 2^k}$.

Output $\lfloor x \times 10^5 \rfloor$.