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?
# | User | Rating |
---|---|---|
1 | tourist | 3757 |
2 | jiangly | 3647 |
3 | Benq | 3581 |
4 | orzdevinwang | 3570 |
5 | Geothermal | 3569 |
5 | cnnfls_csy | 3569 |
7 | Radewoosh | 3509 |
8 | ecnerwala | 3486 |
9 | jqdai0815 | 3474 |
10 | gyh20 | 3447 |
# | User | Contrib. |
---|---|---|
1 | maomao90 | 171 |
2 | awoo | 164 |
3 | adamant | 163 |
4 | TheScrasse | 159 |
5 | maroonrk | 155 |
6 | nor | 154 |
7 | -is-this-fft- | 152 |
8 | Petr | 147 |
9 | orz | 145 |
10 | pajenegod | 144 |
Funny sum :)
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?
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) |
Name |
---|