Problem 388
Distinct Lines

Consider all lattice points (a,b,c) with 0 ≤ a,b,c ≤ 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(1010). Give as your answer the first nine digits followed by the last nine digits.

These problems are part of Project Euler and are licensed under CC BY-NC-SA 2.0 UK