The function
 |
(1)
|
where 
is the number of not necessarily distinct prime factors
of 
,
with 
.
The values of 
for 
,
2, ... are 1, 
,
,
1, 
,
1, 
,
,
1, 1, 
,
,
... (OEIS A008836). The values of 
such that 
are 2, 3, 5, 7, 8, 11, 12, 13, 17, 18, 19, 20,
23, ... (OEIS A026424), while then values such
that 
are 1, 4, 6, 9, 10, 14, 15, 16, 21, 22, 24, ... (OEIS A028260).
The Liouville function is implemented in the Wolfram Language as LiouvilleLambda[n].
The Liouville function is connected with the Riemann zeta function by the equation
 |
(2)
|
(Lehman 1960). It has the Lambert series
 |  |  |
(3)
|
 |  | ![1/2[theta_3(q)-1],](/images/equations/LiouvilleFunction/Inline21.svg) |
(4)
|
where 
is a Jacobi theta function.
The associated Liouville summatory function is denoted 
.
