171
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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:
- $1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $133$, $135$, $141$, $151$, $159$, $163$, $169$, $171$, $\ldots$
Also see
- Previous ... Next: Palindromic Triangular Numbers
- Previous ... Next: Triangular Number Pairs with Triangular Sum and Difference
- Previous ... Next: Pairs of Consecutive Integers with 6 Divisors
- Previous ... Next: Sequence of Palindromic Lucky Numbers
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- Previous ... Next: Lucky Number