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

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The squares -- nine of them.

45

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

The set of positive odd integers.

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).

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

The sum of the first positive odd integers less than 101 is 10,000.

the negative integers are below 0, for example -6.

49

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

666 integers.

Positive integers are greater than zero. Negative integers are less than zero.

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