id	title	challengeType	forumTopicId	dashedName
5900f4ae1000cf542c50ffbf	Problem 320: Factorials divisible by a huge integer	5	301977	problem-320-factorials-divisible-by-a-huge-integer

--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);

function divisibleByHugeInteger() {

  return true;
}

divisibleByHugeInteger();

// solution required