Divisor Sum of 45,946

Example of Divisor Sum of Integer

$\map {\sigma_1} {45 \, 946} = 68 \, 922$

where $\sigma_1$ denotes the divisor sum function.

Proof

We have that:

$45 \, 946 = 2 \times 22 \, 973$

Hence:

\(\ds \map {\sigma_1} {45 \, 946}\)

\(=\)

\(\ds \paren {2 + 1} \times \paren {22 \, 973 + 1}\)

Divisor Sum of Non-Square Semiprime

\(\ds \)

\(=\)

\(\ds 3 \times 22 \, 974\)

\(\ds \)

\(=\)

\(\ds 3 \times \paren {2 \times 3 \times 7 \times 547}\)

\(\ds \)

\(=\)

\(\ds 2 \times 3^2 \times 7 \times 547\)

\(\ds \)

\(=\)

\(\ds 68 \, 922\)

$\blacksquare$