782
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Number
$782$ (seven hundred and eighty-two) is:
- $2 \times 17 \times 23$
- The $23$rd pentagonal number after $1$, $5$, $12$, $22$, $35$, $\ldots$, $477$, $532$, $590$, $651$, $715$:
- $782 = \ds \sum_{k \mathop = 1}^{23} \paren {3 k - 2} = \dfrac {23 \paren {3 \times 23 - 1} } 2$
- The $45$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $392$, $425$, $442$, $477$, $495$, $532$, $551$, $590$, $610$, $651$, $672$, $715$, $737$:
- $782 = \ds \sum_{k \mathop = 1}^{23} \paren {3 k - 2} = \dfrac {23 \paren {3 \times 23 - 1} } 2$