Divisor Sum of 550

Example of Divisor Sum of Integer

$\map {\sigma_1} {550} = 1116$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$550 = 2 \times 5^2 \times 11$

Hence:

\(\ds \map {\sigma_1} {550}\)

\(=\)

\(\ds \paren {2 + 1} \times \frac {5^3 - 1} {5 - 1} \times \paren {11 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds 3 \times \frac {125 - 1} 4 \times 12\)

\(\ds \)

\(=\)

\(\ds 3 \times 31 \times \paren {2^2 \times 3}\)

\(\ds \)

\(=\)

\(\ds 2^2 \times 3^2 \times 31\)

\(\ds \)

\(=\)

\(\ds 1116\)

$\blacksquare$