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On the distributions of sigma(N)/N and N/Phi(N)

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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.

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Rocky Mountain Mathematics Consortium

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Mathematics

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Rocky Mountain Journal of Mathematics

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10.1216/RMJ-2013-43-3-713

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