729

Number
$729$ (seven hundred and twenty-nine) is:
 * $3^6$


 * $1 \, 000 \, 000$ in base $3$


 * The $1$st solution to the approximate Fermat equation $x^3 = y^3 + z^3 \pm 1$:
 * $9^3 = 6^3 + 8^3 + 1$


 * The $1$st cube which can be expressed as the sum of $5$ positive cubes:
 * $729 = 1^3 + 3^3 + 4^3 + 5^3 + 8^3$


 * The larger of the $1$st pair of Smith brothers:
 * $7 + 2 + 8 = 2 + 2 + 2 + 7 + 1 + 3 = 17$, $7 + 2 + 9 = 3 + 3 + 3 + 3 + 3 + 3 = 18$


 * The $2$nd cube which can be expressed as the sum of $3$ positive cubes:
 * $729 = 1^3 + 6^3 + 8^3$


 * The $3$rd $6$th power after $1$, $64$:
 * $729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3$


 * The $3$rd power of $9$ after $(1)$, $9$, $81$:
 * $729 = 9^3$


 * The $6$th power of $3$ after $(1)$, $3$, $9$, $27$, $81$, $243$:
 * $729 = 3^6$


 * The $9$th cube number after $1$, $8$, $27$, $64$, $125$, $216$, $343$, $512$:
 * $729 = 9 \times 9 \times 9$


 * The $27$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $\ldots$, $361$, $400$, $441$, $484$, $529$, $576$, $625$, $676$:
 * $729 = 27 \times 27$


 * The $38$th Smith number after $4$, $22$, $27$, $58$, $\ldots$, $576$, $588$, $627$, $634$, $636$, $645$, $648$, $654$, $663$, $666$, $690$, $706$, $728$:
 * $7 + 2 + 9 = 3 + 3 + 3 + 3 + 3 + 3 = 18$


 * The $46$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $\ldots$, $400$, $432$, $441$, $484$, $500$, $512$, $529$, $576$, $625$, $648$, $675$, $676$:
 * $729 = 3^6$

Also see

 * Period of Reciprocal of 729 is 81