On the numbers of prime factors of square free amicable pairs
Volume 177 / 2017
Acta Arithmetica 177 (2017), 153-167
MSC: 11A99, 11P99.
DOI: 10.4064/aa8327-7-2016
Published online: 18 January 2017
Abstract
Let $s\leq t$ be positive integers. For any square free amicable pair $(m, n)$, we say that $(m ,n)$ is of type $\{s, t\}$ if one of $m,n$ has $s$ prime factors and the other has $t$ prime factors. We prove the non-existence of square free amicable pairs of type $\{s, t\}$ with $s+t\leq 6$. Further, we prove that there are no square free amicable pairs of type $\{2, t\}$ with $t=5, 6, 7, 8$.
