Problem 379

Least common multiple count

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}).

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