Let $p_i$ denote the $i^{th}$ prime number.
Find the smallest positive integer $k$ such that the product $n = p_1 \cdot p_2 \cdots p_k$ satisfies $\sigma(n) > 3n$.
Is there any positive integer $m < n$ satisfying $\sigma(m) > 3m$?
Taken From (Rosen), at the end of the chapter under challenge problems
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