399
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Number
$399$ (three hundred and ninety-nine) is:
- $3 \times 7 \times 19$
- 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:
- $0$, $1$, $2$, $3$, $11$, $27$, $37$, $41$, $73$, $77$, $116$, $154$, $320$, $340$, $399$
- The $43$rd sphenic number after $30$, $42$, $66$, $70$, $\ldots$, $290$, $310$, $318$, $322$, $345$, $354$, $357$, $366$, $370$, $374$, $385$:
- $399 = 3 \times 7 \times 19$
Also see
- Previous ... Next: Numbers not Expressible as Sum of Fewer than 19 Fourth Powers
- Previous ... Next: Sequence of Integers whose Factorial plus 1 is Prime
- Previous ... Next: Sphenic Number
- Next: Lucas-Carmichael Number
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $399$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $399$