perfect number problem

[yohai]

hi everyone,im a 17 year old ,studying pcm in india and i am a bit interested in the subjects that i learn. so a few days ago i heard about smth called perfect numbers. so my question is that why do not we have a prime perfect number?

[KJW]

The aliquot sum of any prime number is 1.

 

[yohai]

can you explain more about the term aliquot sum

[joigus]

As @KJW said, the aliquot sum:

Quote

In number theory, the aliquot sum s(n) of a positive integer n is the sum of all proper divisors of n, that is, all divisors of n other than n itself.

of any prime number is 1, so no prime number can be perfect. Example:

6=1+2+3=1*2*3

[KJW]

15 minutes ago, yohai said:

can you explain more about the term aliquot sum

I was thinking about making the term "aliquot sum" a link to its Wikipedia article, but because it is a policy of science forums not to do people's homework for them, I decided to leave some room for you to do your own research on the problem.

 

[yohai]

3 hours ago, KJW said:

I was thinking about making the term "aliquot sum" a link to its Wikipedia article, but because it is a policy of science forums not to do people's homework for them, I decided to leave some room for you to do your own research on the problem.

 

ok thanks