Open AccessOn the distributions of $\sigma(n)/n$ and $n/\varphi(n)$
Author(s) -
Emre Alkan
Publication year - 2013
Publication title -
the rocky mountain journal of mathematics/rocky mountain journal of mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.374
H-Index - 42
eISSN - 1945-3795
pISSN - 0035-7596
DOI - 10.1216/rmj-2013-43-3-713
Subject(s) - mathematics , sigma , combinatorics , pure mathematics , physics , quantum mechanics
We prove that the distribution functions of sigma(n)/n and n/phi(n) both have super-exponential asymptotic decay when n ranges over certain subsets of integers, which, in particular, can be taken as the set of l-free integers not divisible by a thin subset of primes