159

Number
$159$ (one hundred and fifty-nine) is:


 * $3 \times 53$


 * The $2$nd positive integer after $79$ which cannot be expressed as the sum of fewer than $19$ fourth powers:
 * $159 = 14 \times 1^4 + 4 \times 2^4 + 3^4$


 * The $5$th Woodall number after $1$, $7$, $23$, $63$:
 * $159 = 5 \times 2^5 - 1$


 * The $6$th positive integer after $1$, $7$, $102$, $110$, $142$ the sum of whose divisors is a cube:
 * $\map {\sigma_1} {159} = 216 = 6^3$


 * The $32$nd lucky number:
 * $1$, $3$, $7$, $9$, $13$, $15$, $21$, $\ldots$, $115$, $127$, $129$, $133$, $135$, $141$, $151$, $159$, $\ldots$


 * The $61$st and last positive integer after $2$, $3$, $4$, $7$, $8$, $\ldots$, $124$, $136$, $137$, $141$, $142$, $147$ which cannot be expressed as the sum of distinct pentagonal numbers.