Odd Perfect Number

A perfect number N is one in which the sum of its divisors equal N.   This means that first perfect number is 6, because 1, 2, and 3 are its divisors, and when added up are equal to 6.

The problem is that it has yet to be proven whether or not any odd perfect numbers exist.

Chris Kam Suan Khai
Chris Kam Suan Khai's picture
User offline. Last seen 2 years 30 weeks ago. Offline
Joined: 09/21/2011

is it 9 an odd perfect number?


User offline. Last seen 2 years 9 weeks ago. Offline
Joined: 02/08/2012

If the definition is changed and supplemented, I can solve this.

If you do a Summation Notation of n where the upper limit is the Mersenne Prime, you'll end up with the same values. If the upper limit is 127 the value is 8128 which is factored to 2^6*127, a perect number.

If you do 4^n/2 in a summation you'll end up with a 3 in base 4.

So if you do the first summation with one of my primes (43), you'll end up with 946 which is 2*11*43. The two is extra, but the 11 is found with my formula -1. If you do another formula you'll end up with a prime of 174763 which has a summation of 15271140466 and that is factored to 2*43691*174763. Once again the 2 is extra and the 43691 is my -1 function.

There is a problem with this. For it to get the prime and the prime before it, both have to be prime. Otherwise you'll get a prime and a factor of the -1 function.

I have 18 primes so far up to the 99th term. Btw, there is a very distinct pattern to this formula. I'm pretty sure it's possible to detect every prime if you use a cubic formula. But I could be wrong.


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