Divisor Sum of 2016

Example of Divisor Sum of Integer

$\map {\sigma_1} {2016} = 6552$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$2016 = 2^5 \times 3^2 \times 7$

Hence:

\(\ds \map {\sigma_1} {2016}\)

\(=\)

\(\ds \frac {2^6 - 1} {2 - 1} \times \frac {3^3 - 1} {3 - 1} \times \paren {7 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \frac {63} 1 \times \frac {26} 2 \times 8\)

\(\ds \)

\(=\)

\(\ds \paren {3^2 \times 7} \times 13 \times 2^3\)

\(\ds \)

\(=\)

\(\ds 2^3 \times 3^2 \times 7 \times 13\)

\(\ds \)

\(=\)

\(\ds 6552\)

$\blacksquare$