How many of the numbers from 1 to 30 have exactly four positive divisors?

A number has exactly four divisors in only two ways: it is $p\times q$ for two different primes (divisors 1, $p,q,pq$), or it is $p^3$ (divisors 1, $p,p^2,p^3$). Up to 30 the first kind gives 6, 10, 14, 15, 21, 22 and 26 — seven numbers. The second kind gives $8=2^3$ and $27=3^3$. Altogether 7 + 2 = 9. Forgetting the cubes and listing only the products of two primes leaves 7, which is the commonest slip here.