Elementary Proof of No Odd Perfect Numbers [closed]
Solution 1:
I see (3.6) is wrong:
The third term, $\prod _{i=1} ^ m p_i \sigma (p_i ^ {a_i-1})$ is as one expects, the rest. It includes those divisors that have at least one $p_1$ but also include some other prime or primes.
I don't think this is right, there's no way from this we could get, say, $p_1p_2$ (with $m \ge 3$) since $p_3$ is always in the product.