6561

Number
$6561$ (six thousand, five hundred and sixty-one) is:


 * $3^8$


 * The $3$rd positive integer after $1$, $625$ whose $4$th root equals the number of its divisors:
 * $\map {\sigma_0} {6561} = 9 = \sqrt [4] {6561}$


 * The $3$rd eighth power after $1$, $256$:
 * $6561 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3$


 * The $4$th power of $9$ after $(1)$, $9$, $81$, $729$:
 * $6561 = 9^4$


 * The $8$th power of $3$ after $(1)$, $3$, $9$, $27$, $81$, $243$, $729$, $2187$:
 * $6561 = 3^8$


 * The $9$th fourth power after $1$, $16$, $81$, $256$, $625$, $1296$, $2401$, $4096$:
 * $6561 = 9 \times 9 \times 9 \times 9$


 * The $81$st square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $5041$, $5184$, $5329$, $5476$, $5625$, $5776$, $5929$, $6084$, $6241$, $6400$
 * $6561 = 81 \times 81$