21. [11] Call a number overweight if it has at least three positive integer divisors (including 1 and the number), and call a number obese if it has at least four positive integer divisors (including 1 and the number). How many positive integers between 1 and 200 are overweight, but not obese?
Answer: 6 A positive integer is overweight, but not obese, if it has exactly 3 factors - this can only happen if that integer is the square of a prime. (If two primes, $p$ and $q$, divide the number, then $p, q$, $p q$, and 1 all divide it, making it at least obese). So, the integers less than 200 which are squares of a prime are the squares of $2,3,5,7,11$, and 13 .