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 | Benq | 3792 |
| 2 | VivaciousAubergine | 3647 |
| 3 | Kevin114514 | 3611 |
| 4 | jiangly | 3583 |
| 5 | strapple | 3515 |
| 6 | tourist | 3470 |
| 7 | Radewoosh | 3415 |
| 8 | Um_nik | 3376 |
| 9 | maroonrk | 3361 |
| 10 | XVIII | 3345 |
| Страны | Города | Организации | Всё → |
| № | Пользователь | Вклад |
|---|---|---|
| 1 | Qingyu | 162 |
| 2 | adamant | 148 |
| 3 | Um_nik | 146 |
| 4 | Dominater069 | 143 |
| 5 | errorgorn | 141 |
| 6 | cry | 138 |
| 7 | Proof_by_QED | 136 |
| 8 | YuukiS | 135 |
| 9 | chromate00 | 134 |
| 10 | soullless | 133 |
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.