Abstract
For each positive-integer valued arithmetic function , let denote the image of , and put and . Recently Ford, Luca, and Pomerance showed that is infinite, where denotes Euler’s totient function and is the usual sum-of-divisors function. Work of Ford shows that as . Here we prove a result complementary to that of Ford et al. by showing that most -values are not -values, and vice versa. More precisely, we prove that, as ,
Citation
Kevin Ford. Paul Pollack. "On common values of $\phi(n)$ and $\sigma(m)$, II." Algebra Number Theory 6 (8) 1669 - 1696, 2012. https://doi.org/10.2140/ant.2012.6.1669
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