Funny sum :)

Revision en4, by hmmmmm, 2024-02-12 19:55:06

Let $$$p_i$$$ — minimal prime divisor of $$$i$$$.

$$$s(n) = \sum_{i=2}^n \lceil \log_2(p_i) \rceil$$$.

I checked that $$$s(n) \leq 4 \cdot n$$$ if $$$n \leq 10^{10}$$$.

What is actual estimation of this sum?

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  Rev. Lang. By When Δ Comment
en4 English hmmmmm 2024-02-12 19:55:06 1 Tiny change: 'lceil \log2(p_i) \rc' -> 'lceil \log_2(p_i) \rc'
en3 English hmmmmm 2024-02-12 19:52:57 0 (published)
en2 English hmmmmm 2024-02-12 19:49:38 5 Tiny change: 'n \leq 10^9$.\n\nWhat' -> 'n \leq 10^{10}$.\n\nWhat' (saved to drafts)
en1 English hmmmmm 2024-02-12 19:14:31 210 Initial revision (published)