Divisor Sum of 122,410

Example of Divisor Sum of Integer

$\map {\sigma_1} {122 \, 410} = 220 \, 356$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$122 \, 410 = 2 \times 5 \times 12 \, 241$

Hence:

\(\ds \map {\sigma_1} {122 \, 410}\)

\(=\)

\(\ds \paren {2 + 1} \times \paren {5 + 1} \times \paren {12 \, 241 + 1}\)

Divisor Sum of Square-Free Integer

\(\ds \)

\(=\)

\(\ds 3 \times 6 \times 12 \, 242\)

\(\ds \)

\(=\)

\(\ds 3 \times \paren {2 \times 3} \times \paren {2 \times 6121}\)

\(\ds \)

\(=\)

\(\ds 2^2 \times 3^2 \times 6121\)

\(\ds \)

\(=\)

\(\ds 220 \, 356\)

$\blacksquare$