On the Order of Magnitude of the Divisor Function

Authors
Weber, Michel
Citation
Weber, Michel, On the Order of Magnitude of the Divisor Function, Acta mathematica Sinica. English series (Print) , 22(2), 2006, pp. 377-382
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
22
Issue
2
Year of publication
2006
Pages
377 - 382
Database
ACNP
SICI code
Abstract
Let D be an increasing sequence of positive integers, and consider the divisor functions: d(n,D)=.d|nd.D,d.n.1,d2(n,D)=.[d,.]|nd,..D,[d,.].n.1, whe re [d, .] = l.c.m.(d, .). A probabilistic argument is introduced to evaluate the series ..n=1.nd(n,D) and ..n=1.nd2(n,D)