How to know if the number of divisors in a determined range for a number is odd or even

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I would like to know if the number of divisors for the number in a determined range is odd or even without counting the divisors, I think the question is a little tad fuzzy, thus, I will supply the question with an example . Suppose we have n = 7 and b = 24, Is the number of divisors for b in range 1 to n odd or even ? in our example we have : 1,2,3,4,6 then we have five divisors, so the number is odd, we just omitted the rest divisors { 8, 12, 24 } because they are out of the range . Is there such a method to solve this matter ? Thank you !