--description--

Let $N(i)$ be the smallest integer $n$ such that $n!$ is divisible by $(i!)^{1234567890}$

Let $S(u) = \sum N(i)$ for $10 ≤ i ≤ u$.

$S(1000)=614\,538\,266\,565\,663$.

Find $S(1\,000\,000)\bmod {10}^{18}$.

--hints--

divisibleByHugeInteger() should return 278157919195482660.

assert.strictEqual(divisibleByHugeInteger(), 278157919195482660);

--seed--

--seed-contents--

function divisibleByHugeInteger() {

  return true;
}

divisibleByHugeInteger();

--solutions--

// solution required