A Fermat Pseudoprime to base 2, denoted psp(2), i.e., a Composite Odd Integer such that
Pomerance has shown that the number of Poulet numbers less than for sufficiently large satisfy
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.
See also Fermat Pseudoprime, Pseudoprime, Super-Poulet Number
References
Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 28-29, 1994.
Pomerance, C.; Selfridge, J. L.; and Wagstaff, S. S. Jr. ``The Pseudoprimes to .'' Math. Comput.
35, 1003-1026, 1980. Available electronically from
ftp://sable.ox.ac.uk/pub/math/primes/ps2.Z.
Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 115-117, 1993.
Sloane, N. J. A. Sequence
A001567/M5441
in ``An On-Line Version of the Encyclopedia of Integer Sequences.''
http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.
The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.