67

Number
$67$ (sixty-seven) is:


 * The $19$th prime number, after $2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61$


 * The $16$th lucky number:
 * $1, 3, 7, 9, 13, 15, 21, 25, 31, 33, 37, 43, 49, 51, 63, 67, \ldots$


 * The $31$st integer $n$ such that $2^n$ contains no zero in its decimal representation:
 * $2^{67} = 147 \, 573 \, 952 \, 589 \, 676 \, 412 \, 928$


 * The $13$th positive integer $n$ after $5, 11, 17, 23, 29, 30, 36, 42, 48, 54, 60, 61$ such that no factorial of an integer can end with $n$ zeroes.


 * The $24$th positive integer which is not the sum of $1$ or more distinct squares:
 * $2, 3, 6, 7, 8, 11, 12, 15, 18, 19, 22, 23, 24, 27, 28, 31, 32, 33, 43, 44, 47, 48, 60, 67, \ldots$


 * The $39$th positive integer after $2, 3, 4, 7, 8, \ldots, 50, 54, 55, 59, 60, 61, 65, 66$ which cannot be expressed as the sum of distinct pentagonal numbers.