Three times Number whose Sigma is Square/Proof 2

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Theorem

Let $n \in \Z_{>0}$ be a positive integer.

Let the $\sigma$ value of $n$ be square.

Let $3$ not be a divisor of $n$.


Then the $\sigma$ value of $3 n$ is square.


Proof

From Numbers whose $\sigma$ is Square:

$\sigma \left({3}\right) = 4 = 2^2$


The result follows as a specific instance of Product of Coprime Numbers whose Sigma is Square has Square Sigma.

$\blacksquare$