Відео

Point of Clarification: I am not claiming that σ(n) cannot contain a multiple of 2. IF I was, it would mean I am arguing that σ(n) cannot be even, but that is not the case given that the identity for both primes and perfect numbers in the sigma function are even, in other words primes (aside from 2) and perfect numbers always result in an even sigma sum. I am stating that the sigma sum σ(n) cannot be the even positive integer 2. If you're not convinced, grab a pen and piece of paper and start calculating σ(n) for all positive integers starting with the smallest positive integer of 1 and let me when you think you'll find a positive integer whose sum of divisors will add up to a total of 2. Go ahead...I'll wait ;)...shouldn't take long to understand what I'm claiming. (This post was inspired by a comment that claimed I was trying to say σ(n) can't contain a multiple of 2. (I think I know what my next video post will be about - a spotlight on the sum-of-divisors function)

Point of Clarification: I am not claiming that σ(n) cannot contain a multiple of 2. IF I was, it would mean I am arguing that σ(n) cannot be even, but that is not the case given that the identity for both primes and perfect numbers in the sigma function are even, in other words primes (aside from 2) and perfect numbers always result in an even sigma sum. I am stating that the sigma sum σ(n) cannot be the even positive integer 2. If you're not convinced, grab a pen and piece of paper and start calculating σ(n) for all positive integers starting with the smallest positive integer of 1 and let me when you think you'll find a positive integer whose sum of divisors will add up to a total of 2. Go ahead...I'll wait ;)...shouldn't take long to understand what I'm claiming. (This post was inspired by a comment that claimed I was trying to say σ(n) can't contain a multiple of 2. (I think I know what my next video post will be about - a spotlight on the sum-of-divisors function)

Something worth pondering might be that presenting something and claiming that it doesn't exist, is already prima facie evidence of it's existence! ;) Even 'infinity' exists! Wanna see it again; >>>> infinity. See?