842 
Ea 1 
(= > aes = =. Fi,) Fea) 
tt me L (A NAC ml 
pam) pm 0,2, nl, 
and consequently 
1 jd 
bm(n,+n,)ema,mte1t «2 flv | amaynty? 
spe es: ESO 
rl 
= Fd) F.(d,)= 
d,d,<« hn,In,! log « fe log « : 
as sm 9, m 
d,d,=l om, ERS 
which was to be proved. 
Mathematics. — “On an arithmetical function connected with the 
decomposition of the positive integers into prime factors.” II. 
(Continued and concluded.) By J. G. vaN DER Corput. (Com- 
municated by Prof. J.-C. Krorver). 
(Communicated in the meeting of June 24, 1916). 
Lemma. ®) The number of (positive integral) divisors of the 
positive integer v satisfies the relation 
Pe Ulett OF (0) 8 
div 
for every u > 0. 
Proof. If v > 2 decomposed into prime factors be equal to 
vs dip 
ple 
we have 
1) This proposition occurs for the first time in Rurar: Ueber die auflösbaren 
Gleichungen von der Form w+ ux-+ v= 0 [Acta mathematica, Bd. VII (1885), 
pages 173—186], pages 181—183, with a proof similar to this one. This 
proof has been borrowed of E. Lanpavu. Ueber die Anzahl der Gitterpunkte in 
gewissen Bereichen [Nachrichten von der Königlichen Gesellschaft der Wissen- 
schaften zu Göttingen, mathematisch-physikalische Klasse (1912), pages 687—771], 
page 716. In his “Handbuch der Lehre von der Verteilung der Primzahlen,” 
I. p. 220, he gives the by far sharper relation : 
If 5 be positive, £ = £ (3) fitly chosen and « an integer > &, we have 
(1+d)loga 
Sie log log « 
dix 
