28

Number
$28$ (twenty-eight) is:


 * $2^2 \times 7$


 * The $7$th triangular number after $1, 3, 6, 10, 15, 21$:
 * $28 = 1 + 2 + 3 + 4 + 5 + 6 + 7 = \dfrac {7 \times \left({7 + 1}\right)} 2$
 * Hence there are $28$ dominoes in a standard set.


 * The $4$th hexagonal number after $1, 6, 15$:
 * $28 = 1 + 5 + 9 + 13 = 4 \left({2 \times 4 - 1}\right)$


 * The $2$nd perfect number after $6$:
 * $28 = 1 + 2 + 4 + 7 + 14 = \sigma \left({28}\right) - 28 = 4 \times 7 = 2^{3 - 1} \left({2^3 - 1}\right)$


 * The $3$rd Ore number after $1, 6$:
 * $\dfrac {28 \times \tau \left({28}\right)} {\sigma \left({28}\right)} = 3$


 * The $6$th semiperfect number after $6, 12, 18, 20, 24$:
 * The $3$rd primitive semiperfect number after $6, 20$:
 * $28 = 1 + 2 + 4 + 7 + 14$


 * The $12$th Ulam number after $1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26$:
 * $28 = 2 + 26$


 * The $3$rd Keith number after $14, 19$:
 * $2, 8, 10, 18, 28, \ldots$


 * The $7$th happy number after $1, 7, 10, 13, 19, 23$:
 * $28 \to 2^2 + 8^2 = 4 + 64 = 68 \to 6^2 + 8^2 = 36 + 64 = 100 \to 1^2 + 0^2 + 0^2 = 1$


 * The $5$th term of Göbel's sequence after $1, 2, 3, 5, 10$:
 * $28 = \left({1 + 1^2 + 2^2 + 3^2 + 5^2 + 10^2}\right) / 5$


 * The $12$th even number after $2, 4, 6, 8, 10, 12, 14, 16, 20, 22, 26$ which cannot be expressed as the sum of $2$ composite odd numbers.


 * The only perfect number which is the sum of equal powers of exactly $2$ positive integers:
 * $28 = 1^3 + 3^3$


 * The $17$th after $1, 2, 4, 5, 6, 8, 9, 12, 13, 15, 16, 17, 20, 24, 25, 27$ of the $24$ positive integers which cannot be expressed as the sum of distinct non-pythagorean primes.


 * The $20$th integer $n$ after $0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 13, 14, 15, 16, 18, 19, 24, 25, 27$ such that $2^n$ contains no zero in its decimal representation:
 * $2^{28} = 268 \, 435 \, 456$


 * The $15$th positive integer which is not the sum of $1$ or more distinct squares:
 * $2, 3, 6, 7, 8, 11, 12, 15, 18, 19, 22, 23, 24, 27, 28, \ldots$

Also see

 * Perfect Number which is Sum of Equal Powers of Two Numbers