Zentralblatt MATH

Publications of (and about) Paul Erdös
Zbl.No:  346.10033
Autor:  Erdös, Paul; Nicolas, J.L.
Title:  Propriétés probabilistes des diviseurs d'un nombre. (Probabilistic properties of the divisors of a number.) (In French)
Source:  Asterisque 41-42, 203-214 (1977).
Review:  Let n be a natural number and let \Delta (n) denote any of the numbers for which the function gm(n) = m-1 sumd | n, d \leq md assumes its maximum. It is proved that

\Delta (n) \geq \exp (c1 log n/ log log n)

for all n large enough,

\Delta (n) \leq \exp (c2 log n/ log log n)

for infinitely many n's with suitble positive constants c1,c2 and \Delta (n) < n for almost all n.
Reviewer:  I.Z.Ruzsa
Classif.:  * 11K65 Arithmetic functions (probabilistic number theory)
                   11N05 Distribution of primes

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