33

Number
$33$ (thirty-three) is:


 * $3 \times 11$


 * The $11$th semiprime after $4, 6, 9, 10, 14, 15, 21, 22, 25, 26$:
 * $33 = 3 \times 11$


 * The $10$th lucky number:
 * $1, 3, 7, 9, 13, 15, 21, 25, 31, 33, \ldots$


 * The $1$st of the smallest triple of $3$ consecutive semiprimes:
 * $33, 34, 35$


 * The sum of the first $4$ factorials:
 * $33 = 1 + 2 + 6 + 24 = 1! + 2! + 3! + 4!$


 * The largest integer which cannot be expressed as the sum of distinct triangular numbers.


 * The $11$th, and probably largest, integer $n$ after $0, 1, 2, 3, 4, 5, 6, 7, 9, 18$ such that both $2^n$ and $5^n$ have no zeroes in their decimal representation:
 * $2^{33} = 8 \, 589 \, 934 \, 592$, $5^{33} = 116 \, 415 \, 321 \, 826 \, 934 \, 814 \, 453 \, 125$


 * The $12$th and largest (strictly) positive integer after $1, 2, 3, 4, 6, 7, 9, 10, 12, 15, 18$ which cannot be expressed as the sum of exactly $5$ non-zero squares.


 * The $7$th integer after $0, 1, 3, 5, 7, 9$ which is palindromic in both decimal and binary:
 * $33_{10} = 100 \, 001_2$


 * The smallest natural number solution to $\sigma \left({n}\right) = \sigma \left({n + 2}\right)$:
 * $\sigma \left({33}\right) = 48 = \sigma \left({35}\right)$

Also see

 * Smallest Sequence of Three Consecutive Semiprimes
 * Largest Integer not Sum of Distinct Triangular Numbers
 * Powers of 2 and 5 without Zeroes
 * Integer as Sum of 5 Non-Zero Squares