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<h2>Factorials divisible by a huge integer</h2>
<h3>Problem 320</h3>
<div style="font-size:80%;color:#999;">Published on 15 January 2011 at 10:00 pm [Server Time]</div>
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<p>
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>
</p>
<p>
Let S(<var>u</var>)=∑N(<var>i</var>) for 10 ≤ <var>i</var> ≤ <var>u</var>.
</p>
<p>
S(1000)=614538266565663.
</p>
<p>
Find S(1 000 000) mod 10<sup>18</sup>.
</p>


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