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