A super-Poulet number is a Poulet number whose every divisor d divides
- 2d − 2.
For example 341 is a super-Poulet number: it has positive divisors {1, 11, 31, 341} and we have:
- (211 - 2) / 11 = 2046 / 11 = 186
- (231 - 2) / 31 = 2147483646 / 31 = 69273666
- (2341 - 2) / 341 = 13136332798696798888899954724741608669335164206654835981818117894215788100763407304286671514789484550
The super-Poulet numbers below 10,000 are (sequence A050217 in OEIS):
| n | |
|---|---|
| 1 | 341 = 11 × 31 |
| 2 | 1387 = 19 × 73 |
| 3 | 2047 = 23 × 89 |
| 4 | 2701 = 37 × 73 |
| 5 | 3277 = 29 × 113 |
| 6 | 4033 = 37 × 109 |
| 7 | 4369 = 17 × 257 |
| 8 | 4681 = 31 × 151 |
| 9 | 5461 = 43 × 127 |
| 10 | 7957 = 73 × 109 |
| 11 | 8321 = 53 × 157 |
Read more about Super-Poulet Number: Super-Poulet Numbers With 3 or More Distinct Prime Divisors
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