399

Number
$399$ (three hundred and ninety-nine) is:


 * $3 \times 7 \times 19$


 * The $43$rd sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $290$, $310$, $318$, $322$, $345$, $354$, $357$, $366$, $370$, $374$, $385$:
 * $399 = 3 \times 7 \times 19$


 * The $1$st Lucas-Carmichael number:
 * $\left({3 + 1}\right) \mathrel \backslash \left({399 + 1}\right)$, $\left({7 + 1}\right) \mathrel \backslash \left({399 + 1}\right)$, $\left({19 + 1}\right) \mathrel \backslash \left({399 + 1}\right)$


 * The $5$th positive integer after $79$, $159$, $239$, $319$ which cannot be expressed as the sum of fewer than $19$ fourth powers:
 * $399 = 14 \times 1^4 + 3 \times 2^4 + 3^4 + 4^4$
 * or:
 * $399 = 11 \times 1^4 + 4 \times 2^4 + 4 \times 3^4$


 * The $14$th integer $m$ after $1$, $2$, $3$, $11$, $27$, $37$, $41$, $73$, $77$, $116$, $154$, $320$, $340$ such that $m! + 1$ is prime

Also see