190

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


 * $2 \times 5 \times 19$


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


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


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


 * 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 $11$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 $\tau \left({n}\right) \mathrel \backslash \phi \left({n}\right) \mathrel \backslash \sigma \left({n}\right)$:
 * $\tau \left({190}\right) = 8$, $\phi \left({190}\right) = 72$, $\sigma \left({190}\right) = 360$