20

Number
$20$ (twenty) is:


 * $2^2 \times 5$


 * The $1$st positive integer $n$ such that $6 n + 1$ and $6 n - 1$ are both composite:
 * $6 \times 20 - 1 = 119 = 7 \times 17$, $6 \times 20 + 1 = 121 = 11^2$


 * The $1$st tetrahedral number which is the sum of two tetrahedral numbers:
 * $20 = 10 + 10$


 * The $1$st primitive abundant number:
 * The $3$rd abundant number after $12$, $18$:
 * $1 + 2 + 4 + 5 + 10 = 21 > 20$


 * The $3$rd central binomial coefficient after $2$, $6$:
 * $20 = \dbinom {2 \times 3} 3 := \dfrac {6!} {\paren {3!}^2}$


 * The $3$rd number after $1$, $9$ whose square has a divisor sum which is itself square:


 * The $4$th tetrahedral number, after $1$, $4$, $10$:
 * $20 = 1 + 3 + 6 + 10 = \dfrac {4 \paren {4 + 1} \paren {4 + 2} } 6$


 * The $4$th semiperfect number after $6$, $12$, $18$:
 * The $2$nd primitive semiperfect number after $6$:
 * $20 = 1 + 4 + 5 + 10$


 * The $6$th positive integer after $6$, $9$, $12$, $18$, $19$ whose cube can be expressed as the sum of $3$ positive cube numbers:
 * $20^3 = 7^3 + 14^3 + 17^3$


 * The $9$th even number after $2$, $4$, $6$, $8$, $10$, $12$, $14$, $16$ which cannot be expressed as the sum of $2$ composite odd numbers.


 * The $11$th highly abundant number after $1$, $2$, $3$, $4$, $6$, $8$, $10$, $12$, $16$, $18$:
 * $\map {\sigma_1} {20} = 42$


 * The $13$th after $1$, $2$, $4$, $5$, $6$, $8$, $9$, $12$, $13$, $15$, $16$, $17$ of the $24$ positive integers which cannot be expressed as the sum of distinct non-pythagorean primes.


 * The $13$th positive integer after $2$, $3$, $4$, $7$, $8$, $9$, $10$, $11$, $14$, $15$, $16$, $19$ which cannot be expressed as the sum of distinct pentagonal numbers.


 * The $13$th harshad number after $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $10$, $12$, $18$:
 * $20 = 10 \times 2 = 10 \times \paren {2 + 0}$


 * The $16$th (strictly) positive integer after $1$, $2$, $3$, $4$, $6$, $7$, $8$, $9$, $10$, $12$, $13$, $14$, $18$, $19$ which cannot be expressed as the sum of distinct primes of the form $6 n - 1$


 * $20^3 = 11^3 + 12^3 + 13^3 + 14^3$


 * The number of faces on an icosahedron


 * The number of vertices on a regular dodecahedron


 * The number of different ways of playing the first move in chess

Also see

 * Definition:Vigesimal System


 * Smallest n such that 6 n + 1 and 6 n - 1 are both Composite
 * Cube of 20 is Sum of Sequence of 4 Consecutive Cubes