( 75 ) 



square of which divides / 



JS" [X (/.) = 1 or 0, 

 according to / being without or with quadratic factor; for those 

 ^•'s are the divisors of the greatest number </ tlie square of which 

 divides /, so that 



2ii{k)= :2 ii{k) = lor = 



according to g = l,i.G.l being with or witliout quadratic factors. 

 Hence 



where k passes through every integer the square of which divides 

 mb -\- h. If w^e invert the order of summation, k passes from 1 to 

 [|/.u], and every (x (k) appears as often as there are muUiples of ^' 

 in the progression mb -\- h between 1 and x, i. e. Ai^hjc-^ {x) times. 

 So according to (18) and (19) 



k=l k—l 



where the sign 2' indicates that k has but to pass through the 

 numbers ^ \/x prime to b. Hence 



k= 1 k=i 



k=:\ p 



where j^ passes through every prime number not dividing b; on 

 account of 



nC 



1\_ 1 _ 6 



p 

 we find 



Qb,h(^) = '^-, j^ — + 0(v/.r), . . . (20) 



Pib 

 where p passes through the prime factors of b, so 



"b 



