171

Number
$171$ (one hundred and seventy-one) is:


 * $3^2 \times 19$


 * The second of the $2$nd pair of triangular numbers whose sum and difference are also both triangular:
 * $105 = T_{14}$, $171 = T_{18}$, $105 + 171 = T_{23}$, $171 - 105 = T_{11}$


 * The $1$st of the $6$th pair of consecutive integers which both have $6$ divisors:
 * $\map {\sigma_0} {171} = \map {\sigma_0} {172} = 6$


 * The $7$th palindromic triangular number after $0$, $1$, $3$, $6$, $55$, $66$


 * The $10$th palindromic lucky number:
 * $1$, $3$, $7$, $9$, $33$, $99$, $111$, $141$, $151$, $171$, $\ldots$


 * The $18$th triangular number after $1$, $3$, $6$, $10$, $15$, $21$, $28$, $36$, $45$, $55$, $66$, $78$, $91$, $105$, $120$, $136$, $153$:
 * $171 = \ds \sum_{k \mathop = 1}^{18} k = \dfrac {18 \times \paren {18 + 1} } 2$


 * The $35$th lucky number:
 * $1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $133$, $135$, $141$, $151$, $159$, $163$, $169$, $171$, $\ldots$