Sum of Divisors Formula
Prove that
\[
D
=
(1+p_1+\cdots+p_1^{a_1})
(1+p_2+\cdots+p_2^{a_2})
\cdots
(1+p_r+\cdots+p_r^{a_r}),
\]
where $D$ is the sum of all elements of $\operatorname{div}(n)$, given that
\[
n=p_1^{a_1}p_2^{a_2}\cdots p_r^{a_r},
\]
where $p_i$ are distinct primes given from the Fundamental Theorem of Arithmetic.