Let $$$p_i$$$ — minimal prime divisor of $$$i$$$.
$$$s(n) = \sum_{i=2}^n \lceil \log2(p_i) \rceil$$$.
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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Funny sum :)
Let $$$p_i$$$ — minimal prime divisor of $$$i$$$.
$$$s(n) = \sum_{i=2}^n \lceil \log2(p_i) \rceil$$$.
I checked that $$$s(n) \leq 4 \cdot n$$$ if $$$n \leq 10^{10}$$$.
What is actual estimation of this sum?
Rev. | Lang. | By | When | Δ | Comment | |
---|---|---|---|---|---|---|
en4 | hmmmmm | 2024-02-12 19:55:06 | 1 | Tiny change: 'lceil \log2(p_i) \rc' -> 'lceil \log_2(p_i) \rc' | ||
en3 | hmmmmm | 2024-02-12 19:52:57 | 0 | (published) | ||
en2 | 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 | hmmmmm | 2024-02-12 19:14:31 | 210 | Initial revision (published) |
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