--description--

The function $lcm(a, b)$ denotes the least common multiple of $a$ and $b$.

Let $A(n)$ be the average of the values of $lcm(n, i)$ for $1 ≤ i ≤ n$.

E.g: $A(2) = \frac{2 + 2}{2} = 2$ and $A(10) = \frac{10 + 10 + 30 + 20 + 10 + 30 + 70 + 40 + 90 + 10}{10} = 32$.

Let $S(n) = \sum A(k)$ for $1 ≤ k ≤ n$.

$S(100) = 122\,726$.

Find $S(99\,999\,999\,019)\bmod 999\,999\,017$.

--hints--

averageLCM() should return 106467648.

assert.strictEqual(averageLCM(), 106467648);

--seed--

--seed-contents--

function averageLCM() {

  return true;
}

averageLCM();

--solutions--

// solution required