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The range of the sum-of-proper-divisors function

Volume 168 / 2015

Florian Luca, Carl Pomerance Acta Arithmetica 168 (2015), 187-199 MSC: Primary 11A25; Secondary 11N37. DOI: 10.4064/aa168-2-6


Answering a question of Erdős, we show that a positive proportion of even numbers are in the form $s(n)$, where $s(n)=\sigma (n)-n$, the sum of proper divisors of $n$.


  • Florian LucaSchool of Mathematics
    University of the Witwatersrand
    P.O. Box Wits 2050
    Johannesburg, South Africa
  • Carl PomeranceDepartment of Mathematics
    Dartmouth College
    Hanover, NH 03755-3551, U.S.A.

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