36

Number
$36$ (thirty-six) is:


 * $2^2 \times 3^2$


 * The $3$rd of three $2$-digit integers divisible by both the sum and product of its digits:
 * $36 = \left({3 + 6}\right) \times 4 = \left({3 \times 6}\right) \times 2$


 * The $6$th square number after $1, 4, 9, 16, 25$:
 * $36 = 6 \times 6$


 * The $8$th triangular number after $1, 3, 6, 10, 15, 21, 28$:
 * $36 = 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 = \dfrac {8 \times \left({8 + 1}\right)} 2$


 * The $2$nd number after $1$ to be both square and triangular:
 * $36 = 6^2 = \dfrac {8 \times \left({8 + 1}\right)} 2$


 * The sum of the first $3$ cubes:
 * $36 = 1^3 + 2^3 + 3^3$


 * The $6$th abundant number after $12, 18, 20, 24, 30$:
 * $1 + 2 + 3 + 4 + 6 + 9 + 12 + 18 = 55 > 36$


 * The $7$th highly composite number after $1, 2, 4, 6, 12, 24$:
 * $\tau \left({36}\right) = 9$


 * The $7$th superabundant number after $1, 2, 4, 6, 12, 24$:
 * $\dfrac {\sigma \left({36}\right)} {36} = \dfrac {91} {36} = 2 \cdotp 52 \dot 7$


 * The $8$th semiperfect number after $6, 12, 18, 20, 24, 28, 30$:
 * $36 = 3 + 6 + 9 + 18$


 * The $9$th powerful number after $1, 4, 8, 9, 16, 25, 27, 32$


 * The $13$th Ulam number after $1, 2, 3, 4, 6, 8, 11, 13, 16, 18, 26, 28$:
 * $36 = 8 + 28$


 * The $20$th after $1, 2, 4, 5, 6, 8, 9, 12, 13, 15, 16, 17, 20, 24, 25, 27, 28, 32, 35$ of the $24$ positive integers which cannot be expressed as the sum of distinct non-pythagorean primes.


 * $35$ and $4374$ have the same prime factors between them as $36$ and $4375$, that is: $2$, $3$, $5$ and $7$.


 * The $26$th integer $n$ such that $2^n$ contains no zero in its decimal representation:
 * $2^{36} = 68 \, 719 \, 476 \, 736$


 * The $7$th positive integer $n$ after $5, 11, 17, 23, 29, 30$ such that no factorial of an integer can end with $n$ zeroes.

Also see

 * Prime Factors of 35, 36, 4734 and 4735