22
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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:
-
- $\map {\sigma_1} {22} = 36 = 6^2$
- 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:
- $2$, $3$, $6$, $7$, $8$, $11$, $12$, $15$, $18$, $19$, $22$, $\ldots$
Also see
- Previous ... Next: Numbers Equal to Number of Digits in Factorial
- Previous ... Next: Numbers whose Divisor Sum is Square
- Previous ... Next: Smith Number
- Previous ... Next: Sequence of Palindromic Pentagonal Numbers
- Previous ... Next: Hexagonal Pyramidal Number
- Previous ... Next: Smallest Positive Integer which is Sum of 2 Odd Primes in n Ways
- Previous ... Next: Square of Small-Digit Palindromic Number is Palindromic
- Previous ... Next: Pentagonal Number
- Previous ... Next: Generalized Pentagonal Number
- Previous ... Next: Integer Partition
- Previous ... Next: 91 is Pseudoprime to 35 Bases less than 91
- Previous ... Next: Numbers not Sum of Distinct Squares
- Previous ... Next: Positive Even Integers not Expressible as Sum of 2 Composite Odd Numbers
- Previous ... Next: Semiprime Number
Sources
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $22$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $22$