Divisor Sum of 19,916

Example of Divisor Sum of Integer

$\map {\sigma_1} {19 \, 916} = 37 \, 632$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$19 \, 916 = 2^2 \times 13 \times 383$

Hence:

\(\ds \map {\sigma_1} {19 \, 916}\)

\(=\)

\(\ds \frac {2^3 - 1} {2 - 1} \times \paren {13 + 1} \times \paren {383 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds 7 \times 14 \times 384\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 2^8 \times 3 \times 7^2\)

\(\ds \)

\(=\)

\(\ds 37 \, 632\)

$\blacksquare$