Divisor Sum of 52

Example of Divisor Sum of Integer

$\map {\sigma_1} {52} = 98$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$52 = 2^2 \times 13$

Hence:

\(\ds \map {\sigma_1} {52}\)

\(=\)

\(\ds \frac {2^3 - 1} {2 - 1} \times \frac {13^2 - 1} {13 - 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \frac {8 - 1} 1 \times \frac {169 - 1} {12}\)

\(\ds \)

\(=\)

\(\ds 7 \times 14\)

\(\ds \)

\(=\)

\(\ds 7 \times \paren {2 \times 7}\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 98\)

$\blacksquare$