Divisor Sum of Square-Free Integer/Proof 1

Proof
We have that the Divisor Sum Function is Multiplicative.

From the definition of prime number, each of the prime factors of $n$ is coprime to all other divisors of $n$.

From Divisor Sum of Prime Number, we have:
 * $\map {\sigma_1} {p_i} = p_i + 1$

Hence the result.