Divisor Sum of 14,175

Example of Divisor Sum of Integer

$\map {\sigma_1} {14 \, 175} = 30 \, 008$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$14 \, 175 = 3^4 \times 5^2 \times 7$

Hence:

\(\ds \map {\sigma_1} {14 \, 175}\)

\(=\)

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

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \dfrac {242} 2 \times \dfrac {124} 4 \times 8\)

\(\ds \)

\(=\)

\(\ds 121 \times 31 \times 8\)

\(\ds \)

\(=\)

\(\ds 11^2 \times 31 \times 2^3\)

\(\ds \)

\(=\)

\(\ds 30 \, 008\)

$\blacksquare$