Smallest Number with 2^n Divisors

Theorem

The smallest positive integer with $2^n$ divisors is found by multiplying together the first $n$ numbers in this sequence:

$2, 3, 4, 5, 7, 9, 11, 13, 16, 17, 19, \ldots$

which consists of all the positive integers of the form $p^{\paren {2^k} }$ where $p$ is prime and $k \ge 0$.

Proof

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Sources

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