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How many positive integers are not less than the sum of their divisors?

 Jan 14, 2024
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How many positive integers are not less than the sum of their divisors?      

 

I'd make the argument that any integer can be divided by 1 and by itself.  

From this, we can say that the sum of these divisors of any integer x is x+1. 

Therefore, every integer is less than this particular sum of its divisors. 

Except the integer 1.  1 is divisible only by 1, so the integer is the same as the sum. 

 

So, I conclude that the answer is one ... namely, the integer 1.  

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 Jan 15, 2024

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