Divisor Sum of 14,316

Example of Divisor Sum of Integer

$\map {\sigma_1} {14 \, 316} = 33 \, 432$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$14 \, 316 = 2^2 \times 3 \times 1193$

Hence:

\(\ds \map {\sigma_1} {14 \, 316}\)

\(=\)

\(\ds \frac {2^3 - 1} {2 - 1} \times \paren {3 + 1} \times \paren {1193 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds 7 \times 4 \times 1194\)

\(\ds \)

\(=\)

\(\ds 7 \times 2^2 \times \paren {2 \times 3 \times 199}\)

\(\ds \)

\(=\)

\(\ds 2^3 \times 3 \times 7 \times 199\)

\(\ds \)

\(=\)

\(\ds 33 \, 432\)

$\blacksquare$