190

Number
$190$ (one hundred and ninety) is:


 * $2 \times 5 \times 19$


 * The $10$th hexagonal number after $1$, $6$, $15$, $28$, $45$, $66$, $91$, $120$, $153$:
 * $190 = 1 + 5 + 9 + 13 + 17 + 21 + 25 + 29 + 33 + 37 = 10 \paren {2 \times 10 - 1}$


 * The $11$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 $12$th integer $n$ after $1, 3, 15, 30, 35, 56, 70, 78, 105, 140, 168$ with the property that $\map {\sigma_0} n \divides \map \phi n \divides \map {\sigma_1} n$:
 * $\map {\sigma_0} {190} = 8$, $\map \phi {190} = 72$, $\map {\sigma_1} {190} = 360$


 * The $12$th integer after $7$, $13$, $19$, $35$, $38$, $41$, $57$, $65$, $70$, $125$, $130$ the decimal representation of whose square can be split into two parts which are each themselves square:
 * $190^2 = 36 \, 100$; $36 = 6^2$, $100 = 10^2$


 * The $18$th sphenic number after $30$, $42$, $66$, $70$, $78$, $102$, $105$, $110$, $114$, $130$, $138$, $154$, $165$, $170$, $174$, $182$, $186$:
 * $190 = 2 \times 5 \times 19$


 * The $19$th triangular number after $1$, $3$, $6$, $10$, $15$, $21$, $28$, $36$, $45$, $55$, $66$, $78$, $91$, $105$, $120$, $136$, $153$, $171$:
 * $190 = \ds \sum_{k \mathop = 1}^{19} k = \dfrac {19 \times \paren {19 + 1} } 2$


 * The $30$th happy number after $1$, $7$, $10$, $13$, $19$, $23$, $\ldots$, $91$, $94$, $97$, $100$, $103$, $109$, $129$, $130$, $133$, $139$, $167$, $176$, $188$:
 * $190 \to 1^2 + 9^2 + 0^2 = 1 + 81 + 0 = 82 \to 8^2 + 2^2 = 64 + 4 = 68 \to 6^2 + 8^2 = 36 + 64 = 100 \to 1^2 + 0^2 + 0^2 = 1$