# 222

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## Number

$222$ (two hundred and twenty-two) is:

$2 \times 3 \times 37$

The $2$nd element of the $2$nd set of $4$ positive integers which form an arithmetic sequence which all have the same Euler $\phi$ value:
$\map \phi {216} = \map \phi {222} = \map \phi {228} = \map \phi {234} = 72$

The $12$th second pentagonal number after $2$, $7$, $15$, $26$, $40$, $57$, $77$, $100$, $126$, $155$, $187$:
$222 = \dfrac {12 \paren {3 \times 12 + 1} } 2$

The $13$th of the $17$ positive integers for which the value of the Euler $\phi$ function is $72$:
$73$, $91$, $95$, $111$, $117$, $135$, $146$, $148$, $152$, $182$, $190$, $216$, $222$, $228$, $234$, $252$, $270$

The $20$th sphenic number after $30$, $42$, $66$, $70$, $78$, $102$, $105$, $110$, $114$, $130$, $138$, $154$, $165$, $170$, $174$, $182$, $186$, $190$, $195$:
$222 = 2 \times 3 \times 37$

The $21$st noncototient after $10$, $26$, $34$, $50$, $52$, $58$, $86$, $100$, $116$, $122$, $130$, $134$, $146$, $154$, $170$, $172$, $186$, $202$, $206$, $218$:
$\nexists m \in \Z_{>0}: m - \map \phi m = 222$
where $\map \phi m$ denotes the Euler $\phi$ function

The $24$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$, $\ldots$, $100$, $117$, $126$, $145$, $155$, $176$, $187$, $210$:
$222 = \dfrac {12 \paren {3 \times 12 + 1} } 2$