( 606 ) 
Lim 
co GE 
| = p—! — loglog | 
PE 
The numerical constant at the 
n=o | 
CE Ep”. 
n—_2 7 
right-hand side is evaluated as 
follows. We suppose s >1 and consider again the relation 
o 1 
log f(s) = En = ps, 
From it we have conversely 
= dk 
ll UY 
h=o (— Iek 
= ET olie log € (hs) *), 
where 4 denotes the successive terms of the infinite sequence 
i, 2) 3,5, 6 
) 
formed by writing in ascending order the integers not admitting 
multiple factors, and wj, stands for 
the number of prime factors of 
h (this number 4 itself, if prime, included). 
Thus making s tend to unity we 
ies [= ps logt ()| Sn 
s—=l n=? 
- h=o 
Lim |= prs — log (| eer 
s—l h=2 
and at once find 
= 
n=2 Nn 
1 
so that finally 
Lim 
CSD 
| = p—! — log log | = 
p<e 
have simultaneously 
1 
mn Pee ° 
Nn 
(—1)“ 4 € 
7 log ¢ (h) = — 0.81572, 
L 
= Zp" = 0.31572, 
C — 0.31572 = 0.26150. 
We mentioned this result in order to compare it with a similar 
*) From this formula it is readily seen: 
J (s) of s, we may affirm to exist in the right 
lst that Sys is an analytic function 
half-plane; 2"¢ that the band between 
the parallels s—=5 + in and s=0+ 7, is dotted with an infinity of logarithmic 
discontinuities of f(s); 3'¢ that these discontinuities grow more and more dense as 
we approach the axis of imaginaries, so as to prevent / (s) effectually from being 
continued into the left half-plane. 
