550

Number
$550$ (five hundred and fifty) is:


 * $2 \times 5^2 \times 11$


 * The $9$th primitive abundant number after $20$, $70$, $88$, $104$, $272$, $304$, $368$, $464$:
 * $1 + 2 + 5 + 10 + 11 + 22 + 25 + 50 + 55 + 110 + 275 = 566 > 550$


 * The $10$th pentagonal pyramidal number after $1$, $6$, $12$, $40$, $75$, $126$, $196$, $288$, $405$:
 * $550 = \ds \sum_{k \mathop = 1}^{10} \dfrac {k \paren {3 k - 1} } 2 = \dfrac {10^2 \paren {10 + 1} } 2$


 * The $13$th primitive semiperfect number after $6$, $20$, $28$, $88$, $104$, $272$, $304$, $350$, $368$, $464$, $490$, $496$:
 * $550 = 2 + 11 + 22 + 25 + 50 + 55 + 110 + 275$


 * The smallest positive integer which can be expressed as the sum of $2$ distinct lucky numbers in $26$ different ways