782

Number
$782$ (seven hundred and eighty-two) is:


 * $2 \times 17 \times 23$


 * The $23$rd pentagonal number after $1$, $5$, $12$, $22$, $35$, $\ldots$, $477$, $532$, $590$, $651$, $715$:
 * $782 = \displaystyle \sum_{k \mathop = 1}^{23} \left({3 k - 2}\right) = \dfrac {23 \left({3 \times 23 - 1}\right)} 2$


 * The $45$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $392$, $425$, $442$, $477$, $495$, $532$, $551$, $590$, $610$, $651$, $672$, $715$, $737$:
 * $782 = \displaystyle \sum_{k \mathop = 1}^{23} \left({3 k - 2}\right) = \dfrac {23 \left({3 \times 23 - 1}\right)} 2$