The Dedekind function is defined by the divisor product
(1)

where the product is over the distinct prime factors of , with the special case . The first few values are
(2)
 
(3)
 
(4)
 
(5)
 
(6)
 
(7)
 
(8)
 
(9)
 
(10)
 
(11)

giving 1, 3, 4, 6, 6, 12, 8, 12, 12, 18, ... (OEIS A001615).
Sums for include
(12)
 
(13)

where is the Möbius function.
The Dirichlet generating function is given by
(14)
 
(15)

where is the Riemann zeta function.