Consider all lattice points $(a,b,c)$ with $0 \le a,b,c \le N$.

From the origin $O(0,0,0)$ all lines are drawn to the other lattice points.
Let $D(N)$ be the number of distinct such lines.

You are given that $D(1\,000\,000) = 831909254469114121$.

Find $D(10^{10})$. Give as your answer the first nine digits followed by the last nine digits.