@article{29e06cd56d544a838547721e38f6d02c,
title = "On common values of φ(n) and σ(m). I",
abstract = "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.",
keywords = "Euler's function, sum of divisors function, totients",
author = "Kevin Ford and Paul Pollack",
note = "Funding Information: ∗The first author was supported by NSF Grant DMS-0901339. The second author was supported by an NSF Postdoctoral Fellowship (award DMS-0802970). The research was conducted in part while the authors were visiting the Institute for Advanced Study, the first author supported by grants from the Ellentuck Fund and The Friends of the Institute For Advanced Study. Both authors thank the IAS for its hospitality and excellent working conditions. †Corresponding author. Key words and phrases: Euler{\textquoteright}s function, sum of divisors function, totients. 2000 Mathematics Subject Classification: primary 11N37, secondary 11A25.",
year = "2011",
month = nov,
doi = "10.1007/s10474-011-0087-1",
language = "English (US)",
volume = "133",
pages = "251--271",
journal = "Acta Mathematica Hungarica",
issn = "0236-5294",
publisher = "Springer Netherlands",
number = "3",
}