Super-Poulet number


A super-Poulet number is a Poulet number, or pseudoprime to base 2, whose every divisor d divides
For example, 341 is a super-Poulet number: it has positive divisors and we have:
When is 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 :
n
1341 = 11 × 31
21387 = 19 × 73
32047 = 23 × 89
42701 = 37 × 73
53277 = 29 × 113
64033 = 37 × 109
74369 = 17 × 257
84681 = 31 × 151
95461 = 43 × 127
107957 = 73 × 109
118321 = 53 × 157

Super-Poulet numbers with 3 or more distinct prime divisors

It is relatively easy to get super-Poulet numbers with 3 distinct prime divisors. If you find three Poulet numbers with three common prime factors, you get a super-Poulet number, as you built the product of the three prime factors.
Example:
2701 = 37 * 73 is a Poulet number,
4033 = 37 * 109 is a Poulet number,
7957 = 73 * 109 is a Poulet number;
so 294409 = 37 * 73 * 109 is a Poulet number too.
Super-Poulet numbers with up to 7 distinct prime factors you can get with the following numbers:
For example, 1118863200025063181061994266818401 = 6421 * 12841 * 51361 * 57781 * 115561 * 192601 * 205441 is a super-Poulet number with 7 distinct prime factors and 120 Poulet numbers.