# 231

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## Number

$231$ (two hundred and thirty-one) is:

$3 \times 7 \times 11$

The $11$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $120$, $153$, $190$:
$231 = \displaystyle \sum_{k \mathop = 1}^{11} \paren {4 k - 3} = 11 \paren {2 \times 11 - 1}$

The $21$st triangular number after $1$, $3$, $6$, $10$, $15$, $\ldots$, $136$, $153$, $171$, $190$, $210$:
$231 = \displaystyle \sum_{k \mathop = 1}^{21} k = \dfrac {21 \times \paren {21 + 1} } 2$

The $22$nd sphenic number after $30$, $42$, $66$, $70$, $78$, $102$, $105$, $110$, $114$, $130$, $138$, $154$, $165$, $170$, $174$, $182$, $186$, $190$, $195$, $222$, $230$:
$231 = 3 \times 7 \times 11$

The $44$th lucky number:
$1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $163$, $169$, $171$, $189$, $193$, $195$, $201$, $205$, $211$, $219$, $223$, $231$, $\ldots$