372

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


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


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


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


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


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