540

Number
$540$ (five hundred and forty) is:
 * $2^2 \times 3^3 \times 5$


 * The $15$th heptagonal number after $1$, $7$, $18$, $34$, $55$, $81$, $112$, $148$, $189$, $235$, $286$, $342$, $403$, $469$:
 * $540 = \ds \sum_{k \mathop = 1}^{15} \paren {5 k - 4} = \dfrac {15 \paren {5 \times 15 - 3} } 2$


 * The $27$th positive integer after $64$, $96$, $128$, $144$, $\ldots$, $384$, $400$, $416$, $432$, $448$, $480$, $504$, $512$, $528$ with $6$ or more prime factors:
 * $540 = 2 \times 2 \times 3 \times 3 \times 3 \times 5$


 * The $43$rd untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $\ldots$, $406$, $408$, $426$, $430$, $448$, $472$, $474$, $498$, $516$, $518$, $520$, $530$