Divisor Sum of 650

Example of Divisor Sum of Integer

$\map {\sigma_1} {650} = 1302$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$650 = 2 \times 5^2 \times 13$

Hence:

\(\ds \map {\sigma_1} {650}\)

\(=\)

\(\ds \paren {2 + 1} \times \frac {5^3 - 1} {5 - 1} \times \paren {13 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds 3 \times \frac {125 - 1} 4 \times 14\)

\(\ds \)

\(=\)

\(\ds 3 \times 31 \times \paren {2 \times 7}\)

\(\ds \)

\(=\)

\(\ds 2 \times 3 \times 7 \times 31\)

\(\ds \)

\(=\)

\(\ds 1302\)

$\blacksquare$