Department of Mathematics2024-11-0920130035-759610.1216/RMJ-2013-43-3-7132-s2.0-84882573256https://hdl.handle.net/20.500.14288/3771We 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.pdfMathematicsJournal Articlehttps://doi.org/10.1216/RMJ-2013-43-3-713322719800002Q3NOIR00055