222

Number
$222$ (two hundred and twenty-two) is:
 * $2 \times 3 \times 37$


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


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


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


 * The $2$nd element of the $2$nd set of $4$ positive integers which form an arithmetic progression which all have the same Euler $\phi$ value:
 * $\phi \left({216}\right) = \phi \left({222}\right) = \phi \left({228}\right) = \phi \left({234}\right) = 72$


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