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We know from Ramanujan and Riemann that, $ $ \pi(x) = \operatorname{li}(x) -\tfrac12\operatorname{li}(x^{1/2})-\tfrac13\operatorname{li}(x^{1/3})-\tfrac15\operatorname{li}(x^{1/5}) +\dots$ $ with prime counting function $ \pi(x)$ and logarithmic integral $ \operatorname{li}(x)$ . I was wondering if we truncate the $ \text{RHS}$ up to the second term and consider the function, $ $ F(x)=\frac{\operatorname{li}(x^{1/2})}{\operatorname{li}(x)-\pi(x)}$ $ It turns out it has anRead more