18

Number
$18$ (eighteen) is:
 * $2 \times 3^2$


 * The $2$nd abundant number after $12$:
 * $1 + 2 + 3 + 6 + 9 = 21 > 18$


 * The $3$rd semiperfect number after $6, 12$:
 * $18 = 3 + 6 + 9$


 * The $10$th highly abundant number after $1, 2, 3, 4, 6, 8, 10, 12, 16$:
 * $\sigma \left({18}\right) = 39$


 * The $10$th Ulam number after $1, 2, 3, 4, 6, 8, 11, 13, 16$:
 * $18 = 2 + 16$


 * The $6$th Lucas number after $(2), 1, 3, 4, 7, 11$:
 * $18 = 7 + 11$


 * The $3$rd heptagonal number after $1, 7$:
 * $18 = 1 + 7 + 11 = \dfrac {3 \left({5 \times 3 - 3}\right)} 2$


 * The $3$rd pentagonal pyramidal number after $1, 6$:
 * $18 = 1 + 5 + 12 = \dfrac {3^2 \left({3 + 1}\right)} 2$


 * The $10$th integer $n$ after $0, 1, 2, 3, 4, 5, 6, 7, 9$ such that both $2^n$ and $5^n$ have no zeroes:
 * $2^{18} = 262 \, 144, 5^{18} = 3 \, 814 \, 697 \, 265 \, 625$


 * The $11$th (strictly) positive integer after $1, 2, 3, 4, 6, 7, 9, 10, 12, 15$ which cannot be expressed as the sum of exactly $5$ non-zero squares.


 * The number of distinct pentominoes, if reflections of asymmetrical pentominoes are included in the count.


 * The only number which is twice the sum of its digits:
 * $18 = 2 \times \left({1 + 8}\right)$


 * Equal to the sum of the digits of its cube:
 * $18^3 = 5832$, while $5 + 8 + 3 + 2 = 18$


 * Equal to the sum of the digits of its $6$th power:
 * $18^6 = 34 \, 012 \, 224$, while $3 + 4 + 0 + 1 + 2 + 2 + 2 + 4 = 18$


 * Equal to the sum of the digits of its $7$th power:
 * $18^7 = 612 \, 220 \, 032$, while $6 + 1 + 2 + 2 + 2 + 0 + 0 + 3 + 2 = 18$


 * $18 = 9 + 9$, and its reversal $81 = 9 \times 9$


 * $18^3 = 5832$ and $18^4 = 104 \, 976$, using all $10$ digits from $0$ to $9$ once each between them.


 * The $15$th integer $n$ after $0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16$ such that $2^n$ contains no zero in its decimal representation:
 * $2^{18} = 262 \, 144$


 * The $9$th positive integer which is not the sum of $1$ or more distinct squares:
 * $2, 3, 6, 7, 8, 11, 12, 15, 18, \ldots$


 * The $1$st element of the $1$st pair of integers $m$ whose values of $m \tau \left({m}\right)$ is equal:
 * $18 \times \tau \left({18}\right) = 108 = 27 \times \tau \left({27}\right)$

Also see

 * 18 Pentominoes including Reflections
 * Positive Integers Equal to Sum of Digits of Cube
 * Only Number Twice Sum of Digits is 18