Superabundant Number/Examples/48

Example of Superabundant Number

The abundancy index of $48$ is:

$\dfrac {\map {\sigma_1} {48} } {48} = \dfrac {124} {48} = 2 \cdotp 58 \dot 3$

Proof

\(\ds \map {\sigma_1} {48}\)

\(=\)

\(\ds 124\)

$\sigma_1$ of $48$

\(\ds \leadsto \ \ \)

\(\ds \dfrac {\map {\sigma_1} {48} } {48}\)

\(=\)

\(\ds \dfrac {124} {48}\)

\(\ds \)

\(=\)

\(\ds 2 \cdotp 58 \dot 3\)

$\blacksquare$