854 
the relations thus obtained, added give in the left member 
= fe) 
pm v Sr 
pr v=l 
and in the right member 
us ES | 
bmam w f(v) 0 am 
hloge y=, 1 (log a | : 
ym 
v assuming all the positive integral values for which the congruences 
v=l, gm = |, Li=l 
are possible, i.e. for which the congruence 
zm] =y 
has roots and we conclude 
1 1 
Pies oes 
B f= + Oj, 
prvse loge (log z)° } 
pr v=I 
where 
bm x f(w 
eS en AG), 
h v=l dl 
ym 
zm l ==. 
We have got on far enough now to proceed to proving formula (2) 
for n= 1; we observe that for n=1 
FW) — = /(<) 
gr u pr 
is a finite function of uw, which equals nothing for e,<m and which 
is equal to Ou“) for e, >m, u, representing a constant number 
1 
ee m (m+1) 
In order to prove this, we distinguish four cases: 
UG ae Eig i 
. u . . . . ni 
if — is resolved into prime factors, the smallest exponent of these 
pm 
factors is in this case smaller than m, hence 
F(u)=0 and je — 0, 
i apy 
so that the formula considered is equal to nothing. 
Ds eg = Th, Ci > 
