56

Number

$56$ (fifty-six) is:

$2^3 \times 7$

The $1$st element of the $3$rd pair of integers $m$ whose values of $m \map {\sigma_0} m$ is equal:

$56 \times \map {\sigma_0} {56} = 448 = 64 \times \map {\sigma_0} {64}$

The $6$th integer $n$ after $1, 3, 15, 30, 35$ with the property that $\map {\sigma_0} n \divides \map \phi n \divides \map {\sigma_1} n$:

$\map {\sigma_0} {56} = 8$, $\map \phi {56} = 24$, $\map {\sigma_1} {56} = 120$

The $6$th tetrahedral number, after $1$, $4$, $10$, $20$, $35$:

$56 = 1 + 3 + 6 + 10 + 15 + 21 = \dfrac {6 \paren {6 + 1} \paren {6 + 2} } 6$

The number of integer partitions for $11$:

$\map p {11} = 56$

The $13$th semiperfect number after $6$, $12$, $18$, $20$, $24$, $28$, $30$, $36$, $40$, $42$, $48$, $54$:

$56 = 1 + 2 + 4 + 7 + 14 + 28$

$\ds \map {\sigma_0} { 56 }$

$=$

$\ds 8$

$\ds \map \phi { 56 }$

$=$

$\ds 24$

$\ds \map {\sigma_1} { 56 }$

$=$

$\ds 120$