64

Number
$64$ (sixty-four) is:


 * $2^6$


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


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


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


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


 * The $7$th almost perfect number after $1$, $2$, $4$, $8$, $16$, $32$:
 * $\sigma \left({64}\right) = 127 = 2 \times 64 - 1$


 * 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 sigma values which are strictly increasing:
 * $\sigma \left({61}\right) = 62$, $\sigma \left({62}\right) = 96$, $\sigma \left({63}\right) = 104$, $\sigma \left({64}\right) = 127$


 * 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 $2$nd element of the $3$rd pair of integers $m$ whose values of $m \tau \left({m}\right)$ is equal:
 * $56 \times \tau \left({56}\right) = 448 = 64 \times \tau \left({64}\right)$


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

Also see