data/problems/320.yml
---
:id: 320
:name: Factorials divisible by a huge integer
:url: https://projecteuler.net/problem=320
:content: |+
Let N(<var>i</var>) be the smallest integer <var>n</var> such that <var>n</var>! is divisible by (<var>i</var>!)<sup>1234567890</sup>
Let S(<var>u</var>)=∑N(<var>i</var>) for 10 ≤ <var>i</var> ≤ <var>u</var>.
S(1000)=614538266565663.
Find S(1 000 000) mod 10<sup>18</sup>.