56
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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 $6$, $12$, $18$, $20$, $24$, $28$, $30$, $36$, $40$, $42$, $48$, $54$:
- $56 = 1 + 2 + 4 + 7 + 14 + 28$
Arithmetic Functions on $56$
\(\ds \map {\sigma_0} { 56 }\) | \(=\) | \(\ds 8\) | $\sigma_0$ of $56$ | |||||||||||
\(\ds \map \phi { 56 }\) | \(=\) | \(\ds 24\) | $\phi$ of $56$ | |||||||||||
\(\ds \map {\sigma_1} { 56 }\) | \(=\) | \(\ds 120\) | $\sigma_1$ of $56$ |
Also see
- Previous ... Next: Numbers such that Divisor Count divides Phi divides Divisor Sum
- Previous ... Next: Tetrahedral Number
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $56$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $56$