Divisor Sum of 1648

Example of Divisor Sum of Integer

$\map {\sigma_1} {1648} = 3224$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$1648 = 2^4 \times 103$

Hence:

\(\ds \map {\sigma_1} {1648}\)

\(=\)

\(\ds \dfrac {2^5 - 1} {2 - 1} \times \times \paren {103 + 1}\)

Divisor Sum of Integer

\(\ds \)

\(=\)

\(\ds \dfrac {32} 1 \times 104\)

\(\ds \)

\(=\)

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

\(\ds \)

\(=\)

\(\ds 3224\)

$\blacksquare$