289

Number

$289$ (two hundred and eighty-nine) is:

$17^2$

The larger of the $2$nd pair of consecutive powerful numbers:

$288 = 2^5 \times 3^2$, $289 = 17^2$

$1$, $9$, $25$, $49$, $169$, $289$, $\ldots$

The $9$th Friedman number base $10$ after $25$, $121$, $125$, $126$, $127$, $128$, $153$, $216$:

$289 = \paren {8 + 9}^2$

The $15$th positive integer which cannot be expressed as the sum of a square and a prime:

$1$, $10$, $25$, $34$, $58$, $64$, $85$, $91$, $121$, $130$, $169$, $196$, $214$, $226$, $289$, $\ldots$

The $17$th square number after $1$, $4$, $9$, $16$, $25$, $36$, $49$, $64$, $81$, $100$, $121$, $144$, $169$, $196$, $225$, $256$:

$289 = 17 \times 17$

The $29$th powerful number after $1$, $4$, $8$, $9$, $16$, $25$, $\ldots$, $144$, $169$, $196$, $200$, $216$, $225$, $243$, $256$, $288$

The $54$th lucky number:

$1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $237$, $241$, $259$, $261$, $267$, $273$, $283$, $285$, $289$, $\ldots$