248

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.