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1, 4, 9, 16, 25, 36, 49, 64, 81, 100 -- the square numbers.

Q: What are all the integers less than 103 that have an odd number of positive divisors?

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The squares -- nine of them.

2. That is the only one. And the 11 divisors are 2k where k = 0, 1, ,2, ... , 10

The set of positive odd integers.

The set of positive integers less than 50 is finite (there are 49).The set of all integers less than 50 is infinite, because it includes an infinite number of negative numbers.

No integers are specified in the question, although the answer would be any negative number less than -2 or any positive number greater than 2.

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The squares -- nine of them.

35 is a deficient number because the sum of its proper divisors is less than the number itself.

There are 1,963 such integers. Every factor of a number has a pair. The only time there will be an odd number of factors is if one factor is repeated, ie the number is a perfect square. So the question is really asking: how many positive integers less than 2008 (in the range 1 to 2007) are not perfect squares. √2007 = 44 and a bit (it lies between 44 and 45) So there are 44 integers less than (or equal to) 2007 which are perfect squares → 2007 - 44 = 1963 integers are not perfect squares in the range 1-2007 and have an even number of factors (divisors).

2. That is the only one. And the 11 divisors are 2k where k = 0, 1, ,2, ... , 10

There are 44 positive integers less than 2,010 that have an odd number of factors.

First, you want to know the definition of a perfect number: A perfect number is an integer which is equal to the sum of all its positive integer divisors that are less than itself. Example: The positive integer divisors of 6, less than 6, are 1, 2, and 3. The sum of those divisors is 1 + 2 + 3 = 6. Therefore, 6 is a perfect number. Now, 21 does not meet this definition and therefore is not a perfect number. Let's try it. There are three positive divisors of 21, namely, 1, 3, and 7, that are less than 21, itself. (There are no others.) But the sum of these divisors is 1 + 3 + 7 = 11, which is not equal to 21. Therefore, we confirm that 21 is not a perfect number.

In a list of positive integers less than 20.

The number you are seeking is 36. The divisors are - 36,1,18,2,12,3,9,4,6.

The set of positive odd integers.

533

14 is deficient. It is less than the sum of it's divisors. In mathematics, a deficient number or defective number is a number n for which σ(n) < 2n. Here σ(n) is the sum-of-divisors function: the sum of all positive divisors of n, including n itself Proof.. divisors of 14 are 1,2, and 7 and 14. Now, 2n=28 and and the sum the all the divisors including 14 is 24<28

Five of them.