64

Number
$64$ (sixty-four) is:


 * $2^6$


 * Represented as $100$ in octal and $1 \, 000 \, 000$ in binary.


 * The $1$st positive integer with $6$ or more prime factors:
 * $64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$


 * The $4$th of the $1$st ordered quadruple of consecutive integers that have divisor sums which are strictly increasing:
 * $\map {\sigma_1} {61} = 62$, $\map {\sigma_1} {62} = 96$, $\map {\sigma_1} {63} = 104$, $\map {\sigma_1} {64} = 127$


 * The $2$nd $6$th power after $1$:
 * $64 = 2 \times 2 \times 2 \times 2 \times 2 \times 2$


 * The $2$nd power of $8$ after $(1)$, $8$:
 * $64 = 8^2$


 * The $2$nd element of the $3$rd pair of integers $m$ whose values of $m \map {\sigma_0} m$ is equal:
 * $56 \times \map {\sigma_0} {56} = 448 = 64 \times \map {\sigma_0} {64}$


 * The $3$rd power of $4$ after $(1)$, $4$, $16$:
 * $64 = 4^3$


 * The $4$th cube number after $1$, $8$, $27$:
 * $64 = 4 \times 4 \times 4$


 * The total number of permutations of $r$ objects from a set of $4$ objects, where $1 \le r \le 4$


 * The $6$th power of $2$ after $(1)$, $2$, $4$, $8$, $16$, $32$:
 * $64 = 2^6$


 * The $6$th positive integer which cannot be expressed as the sum of a square and a prime:
 * $1$, $10$, $25$, $34$, $58$, $64$, $\ldots$


 * The $7$th almost perfect number after $1$, $2$, $4$, $8$, $16$, $32$:
 * $\map {\sigma_1} {64} = 127 = 2 \times 64 - 1$


 * The $8$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $49$:
 * $64 = 8 \times 8$


 * The $8$th square after $1$, $4$, $9$, $16$, $25$, $36$, $49$ which has no more than $2$ distinct digits and does not end in $0$:
 * $64 = 8^2$


 * The $11$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $27$, $32$, $36$, $49$


 * The $24$th of $35$ integers less than $91$ to which $91$ itself is a Fermat pseudoprime:
 * $3$, $4$, $9$, $10$, $12$, $16$, $17$, $22$, $23$, $25$, $27$, $29$, $30$, $36$, $38$, $40$, $43$, $48$, $51$, $53$, $55$, $61$, $62$, $64$, $\ldots$

Also see