20

Number
$20$ (twenty) is:


 * $2^2 \times 5$


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


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


 * The $11$th highly abundant number after $1, 2, 3, 4, 6, 8, 10, 12, 16, 18$:
 * $\sigma \left({20}\right) = 42$


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


 * 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 $13$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 $3$rd number after $1, 9$ whose square has a $\sigma$ value which is itself square:


 * The smallest 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 $13$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 number of faces on an icosahedron


 * The number of vertices on a regular dodecahedron

Also see

 * Definition:Vigesimal System


 * Smallest n such that 6 n + 1 and 6 n - 1 are both Composite