Way with words?

Positive integers are the infinite set: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 … (etc.)

but some of those such as 4, 8, 9, 12, 16, 18 are divisible by the square of a prime. If that category is removed we get a reduced set that starts with

1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, … (etc.)

Note: By convention 1 is included in this list.

If x is a positive integer and is not divisible by the square of any prime, then it is an example from that latter set, which is referred to as a square-free, or quadratfrei integer. This is the same as requiring its prime decomposition to contain no repeated factors.

You might also like to read further, as for example this link.

http://en.wikipedia.org/wiki/Quadratic_residue

That x is square-free

You are exactly saying what you exactly said.