Superabundant Number/Examples/240

Example of Superabundant Number

The abundancy index of $240$ is:

$\dfrac {\map {\sigma_1} {240} } {240} = \dfrac {744} {240} = 3 \cdotp 1$

Proof

\(\ds \map {\sigma_1} {240}\)

\(=\)

\(\ds 744\)

$\sigma_1$ of $240$

\(\ds \leadsto \ \ \)

\(\ds \dfrac {\map {\sigma_1} {240} } {240}\)

\(=\)

\(\ds \dfrac {744} {240}\)

\(\ds \)

\(=\)

\(\ds 3 \cdotp 1\)

$\blacksquare$