What number is not a square number and not even?

All non-even numbers are odd.

All squares of even numbers are even.

All squares of odd numbers are odd.

Therefore all numbers which are odd and not the square of an odd number are the solution set.

It contains: {3, 5, 7, 11, 13, 15, 17, 19, 21, 23, 27, 29, 31, ...}