52
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Number
$52$ (fifty-two) is:
- $2^2 \times 13$
- The $4$th term of the $1$st $5$-tuple of consecutive integers have the property that they are not values of the divisor sum function $\map {\sigma_1} n$ for any $n$:
- $\tuple {49, 50, 51, 52, 53}$
- The $3$rd untouchable number after $2$, $5$
- The $5$th Bell number after $(1)$, $1$, $2$, $5$, $15$
- The $5$th noncototient after $10$, $26$, $34$, $50$:
- $\nexists m \in \Z_{>0}: m - \map \phi m = 52$
- where $\map \phi m$ denotes the Euler $\phi$ function
Arithmetic Functions on $52$
\(\ds \map {\sigma_0} { 52 }\) | \(=\) | \(\ds 6\) | $\sigma_0$ of $52$ | |||||||||||
\(\ds \map \phi { 52 }\) | \(=\) | \(\ds 24\) | $\phi$ of $52$ | |||||||||||
\(\ds \map {\sigma_1} { 52 }\) | \(=\) | \(\ds 98\) | $\sigma_1$ of $52$ |
Also see
- Previous ... Next: Untouchable Number
- Previous ... Next: Bell Number
- Previous ... Next: Noncototient
- Previous ... Next: Quintuplets of Consecutive Integers which are not Divisor Sum Values
Historical Note
There are two particular cultural significances for the number $52$:
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $52$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $52$