1485

Number
$1485$ (one thousand, four hundred and eighty-six) is:
 * $3^3 \times 5 \times 11$


 * The first of the $5$th pair of triangular numbers whose sum and difference are also both triangular:
 * $1485 = T_{54}$, $4186 = T_{91}$, $1485 + 4186 = T_{106}$, $4186 - 1485 = T_{73}$


 * The $9$th integer after $1$, $14$, $30$, $105$, $248$, $264$, $418$, $714$ whose divisor sum divided by its Euler $\phi$ value is a square:
 * $\dfrac {\map {\sigma_1} {1485} } {\map \phi {1485} } = \dfrac {2880} {720} = 4 = 2^2$


 * The $54$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $990$, $1035$, $1081$, $1128$, $1176$, $1225$, $1275$, $1326$, $1378$, $1431$:
 * $1485 = \ds \sum_{k \mathop = 1}^{54} k = \dfrac {54 \times \paren {54 + 1} } 2$