$sigma(n)$ is injective?

Question

I was reading about the sum function of divisors $sigma(n)$, and the question arose as to whether this is injective. Does anyone know the answer? in case of being injective some idea for the demonstration? Thanks in advance. And I apologize if it turns out to be an obvious question, I have a suspicion that it is injective but I'm not sure.

DreiCleaner · Accepted Answer

Injective would mean that no two distinct numbers have the same sum of divisors. If there are two distinct numbers whose divisors have the same sum, those would serve as a counterexample to show the function is not injective.
There are many such counterexamples, the smallest is $sigma(6)=sigma(11)=12$

$sigma(n)$ is injective?

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