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).