POTW #15 - April 15, 2024

Contributed by: sawbez

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Difficulty: 10

This problem is tagged with potw, potw2024.

MCR Problem of the Week, April 15, 2024 Edition

The value of the product $$ \prod_{n=1}^{2047} (n \hspace{-0em} \sqrt[23]{2})(n!){(n + 1)}^{n - 2047} $$ can be expressed in the form $a! \times 2^b$ for some integers $a$ and $b$, where $a$ is maximized. Find $a+b$.

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