# real analysis – A problem on the binary representation

Define the number of “1” in the binary representation of $$n$$ as $$sigma(n)$$ , and the number of “0” successive at the end as $$tau(n)$$. (For example, notice that $$(100)_{10}=(1100100)_2$$, then $$sigma(100)=3$$ and $$tau(100)=2$$.) Evaluate $$prod_{n=1}^infty n^{(-1)^{sigma(n)+tau(n)}}.$$