315

Number
$315$ (three hundred and fifteen) is:


 * $3^2 \times 5 \times 7$


 * The $27$th Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $\ldots$, $135$, $144$, $175$, $212$, $216$, $224$, $312$:
 * $315 = 21 \times 15 = 21 \times \left({3 \times 1 \times 5}\right)$


 * The $1$st of the $3$rd ordered triple of consecutive integers after $\left({105, 106, 107}\right)$ and $\left({165, 166, 167}\right)$ that have Euler $\phi$ values which are strictly increasing:
 * $\phi \left({315}\right) = 144$, $\phi \left({316}\right) = 156$, $\phi \left({317}\right) = 316$


 * The magic constant of a magic cube of order $5$, after $1$, $(9)$, $42$, $130$:
 * $315 = \displaystyle \dfrac 1 {5^2} \sum_{k \mathop = 1}^{5^3} k = \dfrac {5 \paren {5^3 + 1} } 2$