496

Number
$496$ (four hundred and ninety-six) is:


 * $2^4 \times 31$


 * The $31$st triangular number after $1, 3, 6, 10, 15, \ldots, 325, 351, 378, 406, 435, 465$:
 * $496 = \displaystyle \sum_{k \mathop = 1}^{31} k = \dfrac {31 \times \left({31 + 1}\right)} 2$


 * The $16$th hexagonal number after $1, 6, 15, 28, 45, 66, 91, 120, 153, 190, 231, 276, 325, 378, 435$:
 * $496 = \displaystyle \sum_{k \mathop = 1}^{16} \left({4 k - 3}\right) = 16 \left({2 \times 16 - 1}\right)$


 * The $3$rd perfect number after $6$ and $28$:
 * $496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248 = 31 \times 16 = \left({2^5 - 1}\right) \left({2^{5 - 1} }\right)$


 * The $12$th primitive semiperfect number after $6$, $20$, $28$, $88$, $104$, $272$, $304$, $350$, $368$, $464$, $490$:
 * $496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248$


 * The $6$th Ore number after $1, 6, 28, 140, 270$:
 * $\dfrac {496 \times \tau \left({496}\right)} {\sigma \left({496}\right)} = 5$