Divisor Sum of 1575

Example of Divisor Sum of Integer

$\map {\sigma_1} {1575} = 3224$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$1575 = 3^2 \times 5^2 \times 7$

Hence:

\(\ds \map {\sigma_1} {1575}\)

\(=\)

\(\ds \dfrac {3^3 - 1} {3 - 1} \times \dfrac {5^3 - 1} {5 - 1} \times \paren {7 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \dfrac {26} 2 \times \dfrac {124} 4 \times 8\)

\(\ds \)

\(=\)

\(\ds 13 \times 31 \times 8\)

\(\ds \)

\(=\)

\(\ds 2^3 \times 13 \times 31\)

\(\ds \)

\(=\)

\(\ds 3224\)

$\blacksquare$