What is the largest number less than 2^64 which has exactly 90 positive divisors ?
№ | Пользователь | Рейтинг |
---|---|---|
1 | tourist | 4009 |
2 | jiangly | 3823 |
3 | Benq | 3738 |
4 | Radewoosh | 3633 |
5 | jqdai0815 | 3620 |
6 | orzdevinwang | 3529 |
7 | ecnerwala | 3446 |
8 | Um_nik | 3396 |
9 | ksun48 | 3390 |
10 | gamegame | 3386 |
Страны | Города | Организации | Всё → |
№ | Пользователь | Вклад |
---|---|---|
1 | cry | 167 |
2 | Um_nik | 163 |
3 | maomao90 | 162 |
3 | atcoder_official | 162 |
5 | adamant | 159 |
6 | -is-this-fft- | 158 |
7 | awoo | 157 |
8 | TheScrasse | 154 |
9 | Dominater069 | 153 |
9 | nor | 153 |
What is the largest number less than 2^64 which has exactly 90 positive divisors ?
Название |
---|
You can find the divisors of 90. Subtract 1 from each of them. And try to assign those divisors-1 as powers to some primes so that the multiplication of assigned divisors = 90. Take an assignment, and find the number as prime1^(divisor1-1) * prime2^(divisor2-1) * ... Take the maximum of those numbers which are less than 2^64.
Good luck!
If only there is another faster way.