Divisor Sum of 19,116

Example of Divisor Sum of Integer

$\map {\sigma_1} {19 \, 116} = 50 \, 820$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$19 \, 116 = 2^2 \times 3^4 \times 59$

Hence:

\(\ds \map {\sigma_1} {19 \, 116}\)

\(=\)

\(\ds \frac {2^3 - 1} {2 - 1} \times \frac {3^5 - 1} {3 - 1} \times \paren {59 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds 7 \times 121 \times 60\)

\(\ds \)

\(=\)

\(\ds 7 \times 11^2 \times \paren {2^2 \times 3 \times 5}\)

\(\ds \)

\(=\)

\(\ds 50 \, 820\)

$\blacksquare$