On the numbers of prime factors of square free amicable pairs
Tom 177 / 2017
Acta Arithmetica 177 (2017), 153-167
MSC: 11A99, 11P99.
DOI: 10.4064/aa8327-7-2016
Opublikowany online: 18 January 2017
Streszczenie
Let 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.
