## Least common multiple count

### Problem 379

Published on Sunday, 8th April 2012, 11:00 am; Solved by 293; Difficulty rating: 70%
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`(10^{6}) = 37429395.

Find `g`(10^{12}).