5565

Number
$5565$ (five thousand, five hundred and sixty-five) is:


 * $3 \times 5 \times 7 \times 53$


 * The $53$rd hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $\ldots$, $4005$, $4186$, $4371$, $4560$, $4950$, $5151$, $5356$:
 * $5565 = \displaystyle \sum_{k \mathop = 1}^{53} \paren {4 k - 3} = 53 \paren {2 \times 53 - 1}$


 * The $105$th triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $4560$, $4656$, $4753$, $4851$, $4950$, $5050$, $5151$, $5253$, $5356$, $5460$:
 * $5565 = \displaystyle \sum_{k \mathop = 1}^{105} k = \dfrac {105 \times \paren {105 + 1} } 2$