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Pencils of rays

Problem 372

Published on Saturday, 18th February 2012, 01:00 pm; Solved by 285; Difficulty rating: 60%

Let R(M, N) be the number of lattice points (x, y) which satisfy M<xN, M<yN and p372_pencilray1.jpg is odd.
We can verify that R(0, 100) = 3019 and R(100, 10000) = 29750422.
Find R(2·106, 109).

Note: p372_pencilray2.gif represents the floor function.