372

Number
$372$ (three hundred and seventy-two) is:


 * $2^2 \times 3 \times 31$


 * The $8$th hexagonal pyramidal number after $1$, $7$, $22$, $50$, $95$, $161$, $252$:
 * $372 = \displaystyle \sum_{k \mathop = 1}^8 k \left({2 k - 1}\right) = \dfrac {8 \left({8 + 1}\right) \left({4 \times 8 - 1}\right)} 6$


 * The $38$th noncototient after $10$, $26$, $34$, $50$, $\ldots$, $290$, $292$, $298$, $310$, $326$, $340$, $344$, $346$, $362$, $366$:
 * $\nexists m \in \Z_{>0}: m - \phi \left({m}\right) = 372$
 * where $\phi \left({m}\right)$ denotes the Euler $\phi$ function


 * The $17$th inconsummate number after $62$, $63$, $65$, $75$, $84$, $95$, $161$, $173$, $195$, $216$, $261$, $266$, $272$, $276$, $326$, $371$:
 * $\nexists n \in \Z_{>0}: n = 372 \times s_{10} \left({n}\right)$


 * The $30$th untouchable number after $2$, $5$, $52$, $88$, $96$, $120$, $124$, $\ldots$, $262$, $268$, $276$, $288$, $290$, $292$, $304$, $306$, $322$, $324$, $326$, $336$, $342$


 * The product with its reversal equals the product of another $3$-digit number with its reversal:
 * $372 \times 273 = 651 \times 156$