Problem
NT-B1-M12-P019 Set 4. Exactly Six Divisors
#19
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Describe all positive integers with exactly \(6\) positive divisors.
Use \( au(n)=(\alpha_1+1)\cdots(\alpha_s+1)\).
If \(n=p_1^{\alpha_1}\cdots p_s^{\alpha_s}\), then \( au(n)=(\alpha_1+1)\cdots(\alpha_s+1)\). We need \(6\). The possibilities are \(6=6\) and \(6=3\cdot2\). Hence \(n=p^5\) or \(n=p^2q\), where \(p,q\) are distinct primes.
Classification task using divisor count.