Divisor Sum of 2835

Example of Divisor Sum of Integer

$\map {\sigma_1} {2835} = 5808$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$2835 = 3^4 \times 5 \times 7$

Hence:

\(\ds \map {\sigma_1} {2835}\)

\(=\)

\(\ds \dfrac {3^5 - 1} {3 - 1} \times \paren {5 + 1} \times \paren {7 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \dfrac {242} 2 \times 6 \times 8\)

\(\ds \)

\(=\)

\(\ds 121 \times 6 \times 8\)

\(\ds \)

\(=\)

\(\ds 11^2 \times \paren {2 \times 3} \times 2^3\)

\(\ds \)

\(=\)

\(\ds 2^4 \times 3 \times 11^2\)

\(\ds \)

\(=\)

\(\ds 5808\)

$\blacksquare$