Sums of number of divisors (ID: 5)
Problem status: not solved
For all positive integers \(n\), let \(\sigma(n)\) be the number of divisors of \(n\). Let
\[ N = \sum_{d | 20160} (\sigma(d))^{2001}. \]Here, \(d\) is a positive integer and a divisor of \(20160\). Find the remainder when \(N\) is divided by \(1000\).
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