The first few Poulet numbers are 341, 561, 645, 1105, 1387, ... (OEIS A001567).
Pomerance et al. (1980) computed all Poulet numbers less than . The numbers less than , , ..., are 0, 3, 22, 78, 245, ... (OEIS A055550).
Pomerance has shown that the number of Poulet numbers less than for sufficiently large satisfy
(Guy 1994).
A Poulet number all of whose divisors satisfy is called a super-Poulet
number. There are an infinite number of Poulet numbers which are not super-Poulet
numbers. Shanks (1993) calls any integer satisfying (i.e., not limited to odd
composite numbers) a Fermatian.