Square-Free Integer

A square-free integer is a whole number that is divisible by no perfect square other than 1, meaning its prime factorization contains no repeated prime factor. For example, 10 (2 times 5) is square-free, while 18 (2 times 3 squared) is not, since 9 divides it evenly. Square-free integers are dense among the positive integers: about 60.79 percent of all positive integers are square-free, a figure equal to 6 over pi squared. Despite this density, no known algorithm can test whether a given integer is square-free in polynomial time, unlike testing whether a number is prime.