1617

Number
$1617$ (one thousand, six hundred and seventeen) is:


 * $3 \times 7^2 \times 11$


 * The $33$rd pentagonal number after $1$, $5$, $12$, $22$, $35$, $\ldots$, $925$, $1001$, $1080$, $1162$, $1247$, $1335$, $1426$, $1520$:
 * $1617 = \ds \sum_{k \mathop = 1}^{33} \paren {3 k - 2} = \dfrac {33 \paren {3 \times 33 - 1} } 2$


 * The $65$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $1335$, $1365$, $1426$, $1457$, $1520$, $1552$:
 * $1617 = \ds \sum_{k \mathop = 1}^{33} \paren {3 k - 2} = \dfrac {33 \paren {3 \times 33 - 1} } 2$