3321

Number

$3321$ (three thousand, three hundred and twenty-one) is:

$3^4 \times 41$

The total of all the entries in a magic square of order $9$, after $1$, $(10)$, $45$, $136$, $325$, $666$, $1225$, $2080$:

$3321 = \ds \sum_{k \mathop = 1}^{9^2} k = \dfrac {9^2 \paren {9^2 + 1} } 2$

The $41$st hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $2145$, $2278$, $2415$, $2556$, $2701$, $2850$, $3003$, $3160$:

$3321 = \ds \sum_{k \mathop = 1}^{41} \paren {4 k - 3} = 41 \paren {2 \times 41 - 1}$

The $81$st triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $2701$, $2775$, $2850$, $2926$, $3003$, $3081$, $3160$, $3240$:

$3321 = \ds \sum_{k \mathop = 1}^{81} k = \dfrac {81 \times \paren {81 + 1} } 2$