Carmichael Function
is the smallest integer such that 
for all 
Relatively Prime to 
. It can bedefined recursively by
Some special values are
 |  |  | |
 | | | |
 | |  | |
 | |  |
for
, and
for
an Odd Prime and 
. The Order of 
(mod ) is at most (Ribenboim 1989). The values of for the first few are 1, 1, 2, 2, 4, 2, 6, 2, 6, 4, 10, 2, 12, ...(Sloane's A002322).See also Modulo Multiplication Group
References
Ribenboim, P. The Book of Prime Number Records, 2nd ed. New York: Springer-Verlag, p. 27, 1989. Riesel, H. ``Carmichael's Function.'' Prime Numbers and Computer Methods for Factorization, 2nd ed. Boston, MA: Birkhäuser, pp. 273-275, 1994. Sloane, N. J. A. SequenceA002322/M0298in ``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. Vardi, I. Computational Recreations in Mathematica. Redwood City, CA: Addison-Wesley, p. 226, 1991.
- Colon Product
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