24 is Smallest Composite Number the Product of whose Proper Divisors is Cube/Mistake

Source Work

1986: David Wells: Curious and Interesting Numbers:

The Dictionary

$24$

1997: David Wells: Curious and Interesting Numbers (2nd ed.):

The Dictionary

$24$

Mistake

The smallest composite number, the product of whose proper divisors is a cube. $2 \times 3 \times 4 \times 6 \times 8 \times 12 = 24^3$.

Correction

There are smaller such numbers.

For example, the product of the proper divisors of $8$ is $8$ itself, which is a cube:

$2 \times 4 = 8 = 2^3$

What it should say is:

The smallest composite number, the product of whose proper divisors is its cube. $2 \times 3 \times 4 \times 6 \times 8 \times 12 = 24^3$.

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $24$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $24$