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 | 3690 |
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 | 174 |
2 | awoo | 164 |
3 | adamant | 162 |
4 | TheScrasse | 160 |
5 | nor | 158 |
6 | maroonrk | 156 |
7 | -is-this-fft- | 152 |
8 | orz | 146 |
9 | pajenegod | 145 |
9 | Petr | 145 |
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?
Name |
---|