How many abundant number can stand in a row???

How many abundant number can stand in a row???

Postby Guest » Sat Aug 25, 2018 6:06 am

Dear math gurus!!!
I am not a mathematician, but only a dilettante, nevertheless the number theory is an unique area of math, where amateurs can create problems as good as professionals.
I tried myself to solve this problem and found that there are unlimited number of triads of consecutive abundant numbers. My prove is the elementary one, it uses some arithmetic knowledge and very beginning of the group theory. It is a constructive proof and the algorithm can create triads of consecutive abundant numbers, but the numbers are enormously large. If you want I can publish my proof. But idea of the proof is very limited and it can not be expanded to x, x+1, x+2, x+3 and longer number sequences.
Good luck, thanks a lot, Lev from Russia

Re: How many abundant number can stand in a row???

Postby phw » Wed Aug 29, 2018 10:19 pm

Apparently, somebody found four consecutive abundant numbers in 2007. It might be worth tracking down some of the citations in if you're interested in pursuing this further. I'm also but an amateur number theorist, and not well versed with the current state of research, however It doesn't look like very much is known about this problem in the general case.

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