845 
Ed) Fy (d) = 0 
and the last case appears only if 
d= g"™ va ad! = gq" vy 
where ¢ is a divisor of 
P=PyPy+++Pn 
ee PS 
consisting of n, prime factors, where g’—=W— is therefore composed 
| q 
of n—n, =n, prime factors and where the product of the integers 
va and vw is equal to v,. In ease (e) we have therefore 
F(a!) == 0, except for hee? 
consequently 
F, (d) F, (@) =f (vd F, (d) 
== (Oy) ear Vy sl, 
== Uh tore Opel, 
hence ms 
= F, (d) F, (@) = =F (ew) 
diu q\P 
fieke d. 
q|P 
a (n,+n,)/ … ey 
P containing exactly —————— different divisors composed of 72, prime 
o Ni n In I 1 | 
nsi Je 
factors, we have 
tr)! 
= 1 mel ’ ef 
qIP dr 
and therefore 
n‚{n 
/ 
2 ES Fd), (d) =f (vu 
(n, -+-n,)! diu 1( ) ( ) ( ) 
u), 
from which relation (5) ensues at once. 
4, BE == Nh ay Nn] 
one of the following conditions at least is in this case satisfied 
a) eam, 
b) erm, 
c) Me Ag Hy 
d) eq’ =m, Ug SR 
so we have 
u 
F(u) = 0 and F’,(d) F, 6 = @ 
De Cu Ee m ) 
in this case one of the numbers e; and eg at least is smaller than 
m, so that again the relations 
