Thinking in a different way what $\ n = xy$ where $\ n, x$ and $\ y$ are natural numbers with $\ x$ and $\ y$ greater than 1 to represent non-prime numbers, I found that we can represent the multiples of $ \ x $ with $ \ sum_ {i = 0} ^ x + xy $ with $ \ y $ natural number
Using this multiple concept, a sieve can be created between two consecutive summations $\ sum_ {i = 0} ^ n$ and $\ sum_ {i = 0} ^ {m}$ where $\ m=n+1$ by subtracting 1,2,3 ... from $\ sum_ {i = 0} ^ {m}$ to $\ m-3$ steps marking the results. The subtraction results are multiples, in the explained mode, of $ \ m-1, m-2, m-3 ..... $
When performing each subtraction, we have a multiple of $ \ m-1, m- 2, m-3 ..... $ and if the difference of $ \ m-1, m-2, m-3 ..... $ to $\ sum_ {i = 0} ^ {m}$ is greater than $ \ m-1, m-2, m-3 ..... $, we can add it and mark the results until we reach $ \ m-1, m-2, m-3 ..... $ or exceed that amount.
At the end of the procedure, the unmarked remaining numbers will be the prime numbers and the powers of 2.
If we make a graph for the equation $ \ n = sum_ {i = 0} ^ x + xy $, where $ \ n $ is the problem number, it corresponds to a hyperbola where considering only the positive whole roots it is found that:
1) Non-prime numbers have some positive integer roots greater than 2
2) Prime numbers have only positive integer roots $ \ x = 1 $ and $ \ x = 2 $
3) The summation has a root where $ \ y = 0 $
4) Powers of 2 have only positive integer root $ \ x = 1 $
Finally, with these criteria multiplicity, multiples of odd numbers behave like conventional multiples, for example multiples of 21 are also 7, instead multiples of even numbers are not always, so for example multiples of 8 are not of 4. No number x below their summation should not be considered multiples and in this system there are no multiples of 2.