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.