3060

Number
$3060$ (three thousand and sixty) is:
 * $2^2 \times 3^2 \times 5 \times 17$


 * The $15$th pentatope number after $1$, $5$, $15$, $35$, $70$, $126$, $210$, $330$, $495$, $715$, $1001$, $1365$, $1820$, $2380$:
 * $3060 = \displaystyle \sum_{k \mathop = 1}^{15} \dfrac {k \paren {k + 1} \paren {k + 2} } 6 = \dfrac {15 \paren {15 + 1} \paren {15 + 2} \paren {15 + 3} } {24}$


 * The $45$th second pentagonal number after $2$, $7$, $15$, $26$, $\ldots$, $1962$, $2072$, $2185$, $2301$, $2420$, $2542$, $2667$, $2795$, $2926$:
 * $3060 = \dfrac {45 \paren {3 \times 45 + 1} } 2$


 * The $90$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $2380$, $2420$, $2501$, $2542$, $2625$, $2667$, $2752$, $2795$, $2882$, $2926$, $3015$:
 * $3060 = \dfrac {45 \paren {3 \times 45 + 1} } 2$