Which numbers have exactly three divisors? Divisors come in pairs (d, n/d), so a number has an odd divisor count only if it's a perfect square, where √n pairs with itself.
For exactly three divisors, n = p² where p is prime. The divisors are 1, p, p².
So "count numbers ≤ N with 3 divisors" becomes "count primes p with p² ≤ N", which means counting primes up to √N. Turning a scary counting problem into a structural fact is pure logic building.