Question 18
A perfect number is an integer that equals half the sum of its positive divisors. For example, because $2 \cdot 28 = 1 + 2 + 4 + 7 + 14 + 28$, $28$ is a perfect number.
a. A square-free integer is an integer not divisible by a square of any prime number. Find all square-free integers that are perfect numbers.
b. Prove that no perfect square is a perfect number.
a. A square-free integer is an integer not divisible by a square of any prime number. Find all square-free integers that are perfect numbers.
b. Prove that no perfect square is a perfect number.