7381

Number
$7381$ (seven thousand, three hundred and eighty-one) is:


 * $11^2 \times 61$


 * The total of all the entries in a magic square of order $11$, after $1$, $(10)$, $45$, $136$, $325$, $666$, $1225$, $2080$, $3321$, $5050$:
 * $7381 = \displaystyle \sum_{k \mathop = 1}^{11^2} k = \dfrac {11^2 \paren {11^2 + 1} } 2$


 * The $61$st hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $5565$, $5778$, $5995$, $6216$, $6441$, $6670$, $6903$, $7140$:
 * $7381 = \displaystyle \sum_{k \mathop = 1}^{61} \paren {4 k - 3} = 61 \paren {2 \times 61 - 1}$


 * The $121$st triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $6786$, $6903$, $7021$, $7140$, $7260$:
 * $7381 = \displaystyle \sum_{k \mathop = 1}^{121} k = \dfrac {121 \times \paren {121 + 1} } 2$