330

Number

$330$ (three hundred and thirty) is:

$2 \times 3 \times 5 \times 11$

The $8$th pentatope number after $1$, $5$, $15$, $35$, $70$, $126$, $210$:

$330 = \ds \sum_{k \mathop = 1}^8 \dfrac {k \paren {k + 1} \paren {k + 2} } 6 = \dfrac {8 \paren {8 + 1} \paren {8 + 2} \paren {8 + 3} } {24}$

The $15$th pentagonal number after $1$, $5$, $12$, $22$, $35$, $51$, $70$, $92$, $117$, $145$, $176$, $210$, $247$, $287$:

$330 = \ds \sum_{k \mathop = 1}^{15} \paren {3 k - 2} = \dfrac {15 \paren {3 \times 15 - 1} } 2$

The $29$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $222$, $247$, $260$, $287$, $301$:

$330 = \dfrac {15 \paren {3 \times 15 - 1} } 2$