3015
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Number
$3015$ (three thousand and fifteen) is:
- $3^2 \times 5 \times 67$
- The $45$th pentagonal number after $1$, $5$, $12$, $22$, $35$, $\ldots$, $1820$, $1926$, $2035$, $2147$, $2262$, $2380$, $2501$, $2625$, $2752$, $2882$:
- $3015 = \ds \sum_{k \mathop = 1}^{45} \paren {3 k - 2} = \dfrac {45 \paren {3 \times 45 - 1} } 2$
- The $89$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $2380$, $2420$, $2501$, $2542$, $2625$, $2667$, $2752$, $2795$, $2882$, $2926$:
- $3015 = \ds \sum_{k \mathop = 1}^{45} \paren {3 k - 2} = \dfrac {45 \paren {3 \times 45 - 1} } 2$