22

Number
$22$ (twenty-two) is:


 * $2 \times 11$


 * The $2$nd integer after $1$ which equals the number of digits in its factorial:
 * $22! = 1 \, 124 \, 000 \, 727 \, 777 \, 607 \, 680 \, 000$
 * which has $22$ digits


 * The $2$nd Smith number after $4$:
 * $2 + 2 = 2 + 1 + 1 = 4$


 * The smallest positive integer which can be expressed as the sum of $2$ odd primes in $3$ ways:
 * $22 = 19 + 3 = 17 + 5 = 11 + 11$


 * The $3$rd pentagonal number after $1$, $5$ which is also palindromic:
 * $22 = 1 + 4 + 7 + 10 = \dfrac {4 \paren {3 \times 4 - 1}} 2$


 * The $3$rd hexagonal pyramidal number after $1$, $7$:
 * $22 = 1 + 6 + 15$


 * The $3$rd number after $1$, $3$ whose divisor sum is square:


 * The $4$th pentagonal number after $1$, $5$, $12$:
 * $22 = 1 + 4 + 7 + 10 = \dfrac {4 \paren {3 \times 4 - 1}} 2$


 * The $6$th palindromic integer after $0$, $1$, $2$, $3$, $11$ whose square is also palindromic integer
 * $22^2 = 484$


 * The $7$th generalized pentagonal number after $1$, $2$, $5$, $7$, $12$, $15$:
 * $22 = \dfrac {4 \paren {3 \times 4 - 1}} 2$


 * The $8$th semiprime after $4$, $6$, $9$, $10$, $14$, $15$, $21$:
 * $22 = 2 \times 11$


 * The $8$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
 * $3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $\ldots$


 * The number of integer partitions for $8$:
 * $\map p 8 = 22$


 * The $10$th even number after $2$, $4$, $6$, $8$, $10$, $12$, $14$, $16$, $20$ which cannot be expressed as the sum of $2$ composite odd numbers.


 * The $11$th positive integer which is not the sum of $1$ or more distinct squares:
 * $2$, $3$, $6$, $7$, $8$, $11$, $12$, $15$, $18$, $19$, $22$, $\ldots$