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

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Q: What are all the integers less than 103 that have an odd number of positive divisors?
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How many positive integers less than 100 have an odd number of positive divisors?

The squares -- nine of them.


Why is 35 deficient is it because its greater to the submultiple of all positive integers?

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


How many positive integers less than 2008 have an even number of divisors?

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).


What are all the positive integers less than 50000 that have 11 divisors?

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


How many positive integers less than 2010 have an odd number of factors?

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


Why 21 is not a perfect number?

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.


Where can you find the number 15?

In a list of positive integers less than 20.


What number has nine divisors and is less than forty?

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


Which has more elements the set of positive odd integers less than 50 or the set of positive even integers less than 50?

The set of positive odd integers.


What is the number of positive integers less than 6000 which are divisible by 5 but not by 9?

533


Is the number 14 a abundant perfect or deficient number?

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


How many positive integers less than 60 are equal to the product of a positive multiple of 5 and an even number?

Five of them.