A superPoulet number is a Poulet number whose every divisor d divides
For example 341 is a superPoulet number: it has positive divisors {1, 11, 31, 341} and we have:
The superPoulet numbers below 10,000 are (sequence A050217 in OEIS):
SuperPoulet numbers with 3 or more distinct prime divisors
It is relatively easy to get superPoulet numbers with 3 distinct prime divisors. If you find three Poulet numbers with three common prime factors, you get a superPoulet 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.
SuperPoulet numbers with up to 7 distinct prime factors you can get with the following numbers:
 { 103, 307, 2143, 2857, 6529, 11119, 131071 }
 { 709, 2833, 3541, 12037, 31153, 174877, 184081 }
 { 1861, 5581, 11161, 26041, 37201, 87421, 102301 }
 { 6421, 12841, 51361, 57781, 115561, 192601, 205441 }
For example 1.118.863.200.025.063.181.061.994.266.818.401 = 6421 * 12841 * 51361 * 57781 * 115561 * 192601 * 205441 is a superPoulet number with 7 distinct prime factors and 120 Poulet numbers.
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