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:
 * $\paren {3 + 1} \divides \paren {399 + 1}$, $\paren {7 + 1} \divides \paren {399 + 1}$, $\paren {19 + 1} \divides \paren {399 + 1}$


 * 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 $15$th integer $m$ such that $m! + 1$ (its factorial plus $1$) is prime:
 * $0$, $1$, $2$, $3$, $11$, $27$, $37$, $41$, $73$, $77$, $116$, $154$, $320$, $340$, $399$