# Problem 441: The inverse summation of coprime couples
For an integer M, we define R(M) as the sum of 1/(p·q) for all the
integer pairs p and q which satisfy all of these conditions: 1 ≤ p <
q ≤ M p + q ≥ M p and q are coprime. We also define S(N) as the sum of
R(i) for 2 ≤ i ≤ N. We can verify that S(2) = R(2) = 1/2, S(10) ≈ 6.9147
and S(100) ≈ 58.2962. Find S(107). Give your answer rounded to four
decimal places.