159

Previous  ... Next

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.

Also see

• Previous  ... Next: Woodall Number
• Previous  ... Next: Numbers not Expressible as Sum of Fewer than 19 Fourth Powers
• Previous  ... Next: Integers whose Divisor Sum is Cube
• Previous: Numbers not Expressible as Sum of Distinct Pentagonal Numbers
• Previous  ... Next: Lucky Number

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $159$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $159$