A Fermat Pseudoprime to base 2, denoted psp(2), i.e., a Composite Odd Integer such that

The first few Poulet numbers are 341, 561, 645, 1105, 1387, ... (Sloane's A001567). Pomerance

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.

**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.

© 1996-9

1999-05-26