In this paper by Ramanujan (http://ramanujan.sirinudi.org/Volumes/published/ram32.pdf), he writes the following formula: $$[x] = \pi_1(x) + \pi_2(x) + \pi_3(x) + \cdots ,$$ what exactly is the function on the LHS? Is it the floor function?
2026-03-30 01:44:57.1774835097
What's this function by Ramanujan?
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The LHS is the floor function, the RHS is $\pi_k(x)$, the number of positive integers which do not exceed $x$ and have exactly $k$ prime factors.