6

Definition
$6$ (Six) is:


 * The second composite number, and the first with distinct prime factors:
 * $6 = 2 \times 3$


 * Hence the first positive integer after $1$ which is not the power of a prime number.


 * The first perfect number, first semiperfect number, and the only number which is the sum and product of the same $3$ distinct numbers:
 * $6 = 1 + 2 + 3 = 1 \times 2 \times 3$


 * The $4$th superabundant number after $1, 2, 4$:
 * $\dfrac {\sigma \left({6}\right)} 6 = 2$


 * The area and semiperimeter of the $3-4-5$ triangle:
 * $6 = \dfrac {3 \times 4} 2 = \dfrac {3 + 4 + 5} 2$


 * The third factorial after $1$ and $2$:
 * $6 = 1 \times 2 \times 3$


 * The second primorial after $1, 2$ (counting $1$ as the zeroth):
 * $6 = 3\# = 2 \times 3$


 * $6 = \sqrt {1^3 + 2^3 + 3^3}$


 * The second hexagonal number:
 * $6 = 1 + 5$


 * The third triangular number:
 * $6 = 1 + 2 + 3$


 * The only triangular number with less than $660$ digits whose square is also triangular:
 * $6^2 = 36 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8$


 * The third automorphic number after $1$ and $5$:
 * $6^2 = 3 \mathbf 6$


 * The $5$th Ulam number after $1, 2, 3, 4$:
 * $6 = 2 + 4$


 * The number of faces of a cube


 * The number of vertices of its dual, the regular octahedron


 * The number of edges of a tetrahedron.

Also see

 * Perfect Number is Sum of Successive Odd Cubes except 6
 * Prime equals Plus or Minus One modulo 6
 * Only Number which is Sum of 3 Factors is 6
 * Triangular Number whose Square is Triangular