[seqfan] Re: A335071 question.

michel.marcus at free.fr michel.marcus at free.fr
Sat May 30 23:14:02 CEST 2020

I had an idea like this: 

Some relevant articles: 




Using 1st article: 

Property 2.2 If ab(n) = k/m with gcd(k, m) = 1, then m|n. 
This follows directly from setting σ(n)/n = k/m. 
Clearly, m|(nk) and since k and m are relatively prime, it must be that m|n. 

Now if ab(n) = ab(n+1) = k/m with gcd(k, m) = 1, then m|n and also m|(n+1). 
But n and n+1 are coprime. So it is not possible. 

But there is a flaw there if they are multiperfect, that is with m=1, then m|n and m|(n+1) . 
So ... 

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