Editing Super-Poulet number (section)

{{Short description|Type of Poulet number}}
In [[number theory]], a '''super-Poulet number''' is a [[Poulet number]], or [[pseudoprime]] to [[Radix|base]] 2, whose every [[divisor]] <math>d</math> divides <math>2^d - 2</math>.

For example, 341 is a super-Poulet number: it has positive divisors (1, 11, 31, 341), and we have:
:(2<sup>11</sup> − 2) / 11 = 2046 / 11 = 186
:(2<sup>31</sup> − 2) / 31 = 2147483646 / 31 = 69273666
:(2<sup>341</sup> − 2) / 341 = 13136332798696798888899954724741608669335164206654835981818117894215788100763407304286671514789484550

When <math> \frac{ \Phi_n(2)}{gcd(n, \Phi_n(2))}</math> is [[Composite number|not prime]], then it and every divisor of it are a pseudoprime to base 2, and a super-Poulet number.
 
The super-Poulet numbers below 10,000 are {{OEIS|id=A050217}}:

{| class="wikitable"
|-
!n
!
|-
| 1
| 341 = 11 &times; 31
|-
| 2
| 1387 = 19 &times; 73
|-
| 3
| 2047 = 23 &times; 89
|-
| 4
| 2701 = 37 &times; 73
|-
| 5
| 3277 = 29 &times; 113
|-
| 6
| 4033 = 37 &times; 109
|-
| 7
| 4369 = 17 &times; 257
|-
| 8
| 4681 = 31 &times; 151
|-
| 9
| 5461 = 43 &times; 127
|-
| 10
| 7957 = 73 &times; 109
|-
| 11
| 8321 = 53 &times; 157
|-
|}