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Least common multiple count

Problem 379

Published on Sunday, 8th April 2012, 11:00 am; Solved by 294

Let f(n) be the number of couples (x,y) with x and y positive integers, x ≤ y and the least common multiple of x and y equal to n.

Let g be the summatory function of f, i.e.: g(n) = ∑ f(i) for 1 ≤ i ≤ n.

You are given that g(106) = 37429395.

Find g(1012).