
COMMENTS

Fermat pseudoprimes are listed in A001567.
The correspondent p for the numbers from the sequence above: 645, 1729, 2821, 3277, 4369, 7957, 10261, 10585, 12801, 13741, 13981, 16705, 18705, 25761, 31621, 49981, 65281, 75361, 83665, 88357, 93961, 101101.
Note that for 22 of the first 80 Poulet numbers, we obtained through this formula another Poulet number!
The formula could be generalized this way: Poulet numbers that can be written as (n + 1)*p^2  n*p, where n is natural, n > 0, and p is another Poulet number.
For n = 1, that formula becomes the formula set out for the sequence above.
For n = 2, that formula becomes 3*p^2  2*p, from which the Poulet numbers 348161 (for p = 341) and 1246785 (for p = 645) were obtained.
For n = 3, that formula becomes 4*p^2  3*p, from which the Poulet number 119273701 (for p = 5461) was obtained.
For n = 4, that formula becomes 5*p^2  4*p, from which the Poulet numbers 2077545 (for p = 645) and 9613297 (for p = 1387) were obtained.
Conjecture: there are infinitely many Poulet numbers that can be written as (n + 1)*p^2  n*p, where n is natural, n > 0, and p is another Poulet number.
Finally, considering, e.g., that for the Poulet number 645, Poulet numbers were obtained for n = 1, 2, 4 (i.e., 831405, 1246785, 2077545), yet another conjecture: For any Poulet number p, there are infinitely many Poulet numbers that can be written as (n + 1)*p^2  n*p, where n is natural, n > 0.
