# Pebrudal's logarithmic sum

Number Theory Level 4

Let $$a$$ and $$b$$ be positive integers such that

$\sum_{n=4}^{2^{200}-1}\left \lfloor \log_{2} n \right \rfloor=a\cdot 2^{b},$

where $$a$$ is an odd integer and $$b$$ is a positive integer. What is $$a+b$$?

This problem is posed by Pebrudal Z.

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