--description--

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.: $g(n) = \sum f(i)$ for $1 ≤ i ≤ n$.

You are given that $g({10}^6) = 37\,429\,395$.

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

--hints--

leastCommonMultipleCount() should return 132314136838185.

assert.strictEqual(leastCommonMultipleCount(), 132314136838185);

--seed--

--seed-contents--

function leastCommonMultipleCount() {

  return true;
}

leastCommonMultipleCount();

--solutions--

// solution required