Divisor Sum of 651

Example of Divisor Sum of Integer

$\map {\sigma_1} {651} = 1024$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$651 = 3 \times 7 \times 31$

Hence:

\(\ds \map {\sigma_1} {651}\)

\(=\)

\(\ds \paren {3 + 1} \paren {7 + 1} \paren {31 + 1}\)

Divisor Sum of Square-Free Integer

\(\ds \)

\(=\)

\(\ds 4 \times 8 \times 32\)

\(\ds \)

\(=\)

\(\ds 2^2 \times 2^3 \times 2^5\)

\(\ds \)

\(=\)

\(\ds 2^{10}\)

\(\ds \)

\(=\)

\(\ds \paren {2^5}^2\)

\(\ds \)

\(=\)

\(\ds 1024\)

$\blacksquare$