Divisor Sum of 8,212,890,625

Example of Divisor Sum of Integer

 * $\map {\sigma_1} {8 \, 212 \, 890 \, 625} = 10 \, 632 \, 324 \, 001$

where $\sigma_1$ denotes the divisor sum.

Proof
From Divisor Sum of Integer
 * $\ds \map {\sigma_1} n = \prod_{i \mathop = 1}^r \frac {p_i^{k_i + 1} - 1} {p_i - 1}$

where $n = \ds \prod_{1 \mathop = 1}^r p_i^{k_i}$ denotes the prime decomposition of $n$.

We have that:
 * $8 \, 212 \, 890 \, 625 = 5^{10} \times 29^2$

Hence: