315

Number

$315$ (three hundred and fifteen) is:

$3^2 \times 5 \times 7$

The $1$st of the $3$rd ordered triple of consecutive integers after $\tuple {105, 106, 107}$ and $\tuple {165, 166, 167}$ that have Euler $\phi$ values which are strictly increasing:

$\map \phi {315} = 144$, $\map \phi {316} = 156$, $\map \phi {317} = 316$

The magic constant of a magic cube of order $5$, after $1$, $(9)$, $42$, $130$:

$315 = \ds \dfrac 1 {5^2} \sum_{k \mathop = 1}^{5^3} k = \dfrac {5 \paren {5^3 + 1} } 2$

The $27$th Zuckerman number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $11$, $12$, $\ldots$, $135$, $144$, $175$, $212$, $216$, $224$, $312$:

$315 = 21 \times 15 = 21 \times \paren {3 \times 1 \times 5}$