The reduced totient function 
, also called the Carmichael lambda function or least
universal exponent function, is the least positive integer 
such that
 |
for every integer 
relatively prime to 
.
Equivalently, 
is the exponent of the modulo
multiplication group modulo 
.
If 
is the prime factorization of 
, then
![lambda(n)=LCM[lambda(p_i^(alpha_i))]_i,](/images/equations/ReducedTotientFunction/NumberedEquation2.svg) |
where 
for an odd prime 
or for 
and 
, while 
for 
. Here 
is the totient function.
This is the standard meaning of Carmichael function. A second function also historically called Carmichael's function is distinguished in that entry.
