Integers whose Tau value equals Cube Root

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Theorem

There are $2$ positive integers whose $\tau$ value equals its cube root:

\(\displaystyle 21 \, 952 = 28^3\) \(:\) \(\displaystyle \map \tau {21 \, 952} = 28\) $\tau$ of $21 \, 952$
\(\displaystyle 64 \, 000 = 40^3\) \(:\) \(\displaystyle \map \tau {64 \, 000} = 40\) $\tau$ of $64 \, 000$


Proof


Sources