Smallest Number with 16 Divisors

Theorem

The smallest positive integer with $16$ divisors is $120$.

Proof

From $\sigma_0$ of $120$:

$\map {\sigma_0} {120} = 16$

The result is a specific instance of Smallest Number with $2^n$ Divisors:

$120 = 2 \times 3 \times 4 \times 5$

$\blacksquare$

Sources

• 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $120$
• 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $120$