Track / Stage 4 / 11 of 340 #271 of 1964

4. A natural number $a$ has 107 different divisors, including 1 and $a$. Find the sum and product of these divisors.

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Answer: 1) $\Sigma_{d}=\frac{a \sqrt[106]{a}-1}{\sqrt[106]{a}-1}$; 2) $\Pi_{d}=\sqrt{a^{107}}$.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.