What is the largest number less than 2^64 which has exactly 90 positive divisors ?
What is the largest number less than 2^64 which has exactly 90 positive divisors ?
№ | Пользователь | Рейтинг |
---|---|---|
1 | tourist | 3843 |
2 | jiangly | 3705 |
3 | Benq | 3628 |
4 | orzdevinwang | 3571 |
5 | Geothermal | 3569 |
5 | cnnfls_csy | 3569 |
7 | jqdai0815 | 3530 |
8 | ecnerwala | 3499 |
9 | gyh20 | 3447 |
10 | Rebelz | 3409 |
Страны | Города | Организации | Всё → |
№ | Пользователь | Вклад |
---|---|---|
1 | maomao90 | 171 |
2 | adamant | 163 |
2 | awoo | 163 |
4 | TheScrasse | 157 |
5 | nor | 153 |
6 | maroonrk | 152 |
6 | -is-this-fft- | 152 |
8 | Petr | 145 |
9 | orz | 144 |
9 | pajenegod | 144 |
Название |
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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.