We define $φ(n)$ as the number of positive integers less than or equal to $n$ that are relatively prime to $n$.

Lets define $S(n) = \sum φ(d)$ over all the divisors of $n$ (i.e. $d$ divides $n$).

Also define $F(n) = \sum S(x)$ where $x$ varies from $1$ to $n$.

Compute the value of $F(999999) + F(888888)$