On common values of φ(n) and σ(m). I

Kevin Ford, Paul Pollack

Research output: Contribution to journalArticlepeer-review


We show, conditional on a uniform version of the prime k-tuples conjecture, that there are x/(log x)1+o(1) numbers not exceeding x common to the ranges of φ and σ. Here φ is Euler's totient function and σ is the sum-of-divisors function.

Original languageEnglish (US)
Pages (from-to)251-271
Number of pages21
JournalActa Mathematica Hungarica
Issue number3
StatePublished - Nov 2011


  • Euler's function
  • sum of divisors function
  • totients

ASJC Scopus subject areas

  • General Mathematics


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