Can't you just call it perfect?

We define a positive integer as a flawless number if is it equal to the sum of all the positive divisors less than itself.

For example, all the positive divisors of 6 are 1, 2, 3, 6. So, 6 is a flawless number because the sum of all the positive divisors less than 6 is 1 + 2 + 3 = 6 1+2+3=6 itself!

What is the smallest flawless number that is larger than 6?


The answer is 28.

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1 solution

If 2 n 1 2^n-1 is prime then ( 2 n 1 ) ( 2 n 1 ) (2^{n-1})(2^n-1) is a flawless number (usually called perfect number ).

Any proof of that?

Peter van der Linden - 4 years, 4 months ago

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It is a bit involved. You could just click on the hyperlink I added.

Ajinkya Shivashankar - 4 years, 4 months ago

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Added later or did I just miss that link? ;)

Peter van der Linden - 4 years, 4 months ago

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