Smallest Number with 16 Divisors
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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): $120$