616

Number
$616$ (six hundred and sixteen) is:
 * $2^3 \times 7 \times 11$


 * The $16$th heptagonal number after $1$, $7$, $18$, $34$, $55$, $81$, $112$, $148$, $189$, $235$, $286$, $342$, $403$, $469$, $540$:
 * $616 = \displaystyle \sum_{k \mathop = 1}^{16} \paren {5 k - 4} = \dfrac {16 \paren {5 \times 16 - 3} } 2$


 * The $19$th integer $n$ after $1$, $3$, $15$, $30$, $35$, $56$, $70$, $78$, $105$, $140$, $168$, $190$, $210$, $248$, $264$, $357$, $420$, $570$ with the property that $\map \tau n \divides \map \phi n \divides \map \sigma n$:
 * $\map \tau {616} = 16$, $\map \phi {616} = 240$, $\map \sigma {616} = 1440$