Geodesic
On the numbers of prime factors of square free amicable pairs
Atsushi Yamagami1
1 Department of Information Systems Science Soka University Tokyo 192-8577, Japan
Acta Arithmetica, Tome 177 (2017) no. 2, pp. 153-167.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 $t=5, 6, 7, 8$.
DOI : 10.4064/aa8327-7-2016
Keywords: leq positive integers square amicable pair say type has prime factors other has prime factors prove non existence square amicable pairs type leq further prove there square amicable pairs type

Atsushi Yamagami 1

1 Department of Information Systems Science Soka University Tokyo 192-8577, Japan 
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Atsushi Yamagami. On the numbers of prime factors of square free amicable pairs. Acta Arithmetica, Tome 177 (2017) no. 2, pp. 153-167. doi : 10.4064/aa8327-7-2016. http://geodesic.mathdoc.fr/articles/10.4064/aa8327-7-2016/

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