Divisor Sum of 2556

Example of Divisor Sum of Integer

$\map {\sigma_1} {2556} = 6552$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$2556 = 2^2 \times 3^2 \times 71$

Hence:

\(\ds \map {\sigma_1} {2556}\)

\(=\)

\(\ds \frac {2^3 - 1} {2 - 1} \times \frac {3^3 - 1} {3 - 1} \times \paren {71 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \frac 7 1 \times \frac {26} 2 \times 72\)

\(\ds \)

\(=\)

\(\ds 7 \times 13 \times \paren {2^3 \times 3^2}\)

\(\ds \)

\(=\)

\(\ds 2^3 \times 3^2 \times 7 \times 13\)

\(\ds \)

\(=\)

\(\ds 6552\)

$\blacksquare$