330

Number
$330$ (three hundred and thirty) is:


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


 * The $15$th pentagonal number after $1, 5, 12, 22, 35, 51, 70, 92, 117, 145, 176, 210, 247, 287$:
 * $330 = \displaystyle \sum_{k \mathop = 1}^{14} \left({3 k - 2}\right) = \dfrac {15 \left({3 \times 15 - 1}\right)} 2$


 * The $29$th generalized pentagonal number after $1, 2, 5, 7, 12, 15, \ldots, 222, 247, 260, 287, 301$:
 * $330 = \dfrac {15 \left({3 \times 15 - 1}\right)} 2$


 * The $8$th pentatope number after $1, 5, 15, 35, 70, 126, 210$:
 * $330 = \displaystyle \sum_{k \mathop = 1}^n \dfrac {k \left({k + 1}\right) \left({k + 2}\right)} 6 = \dfrac {8 \left({8 + 1}\right) \left({8 + 2}\right) \left({8 + 3}\right)} {24}$