248
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Number
$248$ (two hundred and forty-eight) is:
- $2^3 \times 31$
- The $5$th integer after $1$, $14$, $30$, $105$ whose divisor sum divided by its Euler $\phi$ value is a square:
- $\dfrac {\map {\sigma_1} {248} } {\map \phi {248} } = \dfrac {480} {120} = 4 = 2^2$
- The $14$th integer $n$ after $1, 3, 15, 30, 35, 56, 70, 78, 105, 140, 168, 190, 210$ with the property that $\map {\sigma_0} n \divides \map \phi n \divides \map {\sigma_1} n$:
- $\map {\sigma_0} {248} = 8$, $\map \phi {248} = 120$, $\map {\sigma_1} {248} = 480$
- The $16$th untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $146$, $162$, $188$, $206$, $210$, $216$, $238$, $246$
- The $39$th nontotient:
- $\nexists m \in \Z_{>0}: \map \phi m = 248$
- where $\map \phi m$ denotes the Euler $\phi$ function
- The $49$th positive integer $n$ such that no factorial of an integer can end with $n$ zeroes.
Arithmetic Functions on $248$
| \(\ds \map {\sigma_0} { 248 }\) | \(=\) | \(\ds 8\) | $\sigma_0$ of $248$ | |||||||||||
| \(\ds \map \phi { 248 }\) | \(=\) | \(\ds 120\) | $\phi$ of $248$ | |||||||||||
| \(\ds \map {\sigma_1} { 248 }\) | \(=\) | \(\ds 480\) | $\sigma_1$ of $248$ |