Problem
NT-B1-M09-P019 Exactly Two Odd Divisors
#19
★★★☆☆ Level 3 of 5
Describe all positive integers \(n\) with exactly two positive odd divisors.
Consider the odd part of the number.
Let \(n=2^a m\), where \(m\) is odd. The odd divisors of \(n\) are exactly the divisors of \(m\). We need \(\tau(m)=2\), so \(m\) is an odd prime. Therefore \(n=2^a p\), where \(a\ge0\), and \(p\) is an odd prime.
Good inverse problem on the odd part.