Divisor Sum of 33,817,088

Example of Divisor Sum of Integer

$\map {\sigma_1} {33 \, 817 \, 088} = 67 \, 832 \, 061$

where $\sigma_1$ denotes the divisor sum function.

$\ds \map {\sigma_1} n = \prod_{1 \mathop \le i \mathop \le r} \frac {p_i^{k_i + 1} - 1} {p_i - 1}$

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

We have that:

$33 \, 817 \, 088 = 2^9 \times 257^2$

Hence:

$\ds \map {\sigma_1} {33 \, 817 \, 088}$

$=$

$\ds \frac {2^{10} - 1} {2 - 1} \times \frac {257^3 - 1} {257 - 1}$

$\ds $

$=$

$\ds 1023 \times \frac {16 \, 974 \, 592} {256}$

$\ds $

$=$

$\ds 1023 \times 66 \, 307$

$\ds $

$=$

$\ds \paren {3 \times 11 \times 31} \times \paren {61 \times 1087}$

$\ds $

$=$

$\ds 67 \, 832 \, 061$

$\blacksquare$