645

Number
$645$ (six hundred and forty-five) is:


 * $3 \times 5 \times 43$


 * The $15$th octagonal number, after $1$, $8$, $21$, $40$, $65$, $96$, $133$, $176$, $225$, $280$, $341$, $408$, $481$, $560$:
 * $645 = \displaystyle \sum_{k \mathop = 1}^{15} \left({6 k - 7}\right) = 15 \left({3 \times 15 - 2}\right)$


 * The $3$rd Poulet number after $341$, $561$:
 * $2^{645} \equiv 2 \pmod {645}$: $645 = 3 \times 5 \times 43$


 * The $30$th Smith number after $4$, $22$, $27$, $58$, $\ldots$, $454$, $483$, $517$, $526$, $535$, $562$, $576$, $588$, $627$, $634$, $636$:
 * $6 + 4 + 5 = 3 + 5 + 4 + 3 = 15$