mersenneforum.org - View Single Post - Given sigma(n)-n, find the smallest possible n

mart_r · 2013-07-20, 11:34

For example, for large enough odd sigma(n)-n, it's quite easy to find a possible n. It doesn't take long to find a prime p such that q=(sigma(n)-n-1-p) is also prime and n=p*q is found.
The problem now is determining whether this is the smallest solution (mostly it isn't), and how efficiently can it be found?

2013-07-20, 11:34	#1
mart_r Dec 2008 you know...around... 2²·5·31 Posts	Given sigma(n)-n, find the smallest possible n For example, for large enough odd sigma(n)-n, it's quite easy to find a possible n. It doesn't take long to find a prime p such that q=(sigma(n)-n-1-p) is also prime and n=p*q is found. The problem now is determining whether this is the smallest solution (mostly it isn't), and how efficiently can it be found?