[seqfan] Re: A002961: sigma(n)=sigma(n+1).

franktaw at netscape.net franktaw at netscape.net
Tue Jan 5 21:22:48 CET 2010

I'm not sure where you got your 3*10^10 number (the b-file goes to 
2*10^10).  However, any proper multiple of 6 has sigma(n) >2n, while 
6k+|-1 is only divisible by primes 5 or larger.  Just this implies n 
must be at least on the order of 5*10^9 (see A047802).  Since hits for 
large numbers are going to be rare, and abundant numbers prime to 6 are 
rare until n is quite large, I would not be ready to conjecture 
non-existence until testing up to 10^50 or so.  This will of course 
require something better than a brute-force search.

Franklin T. Adams-Watters

-----Original Message-----
From: zak seidov <zakseidov at yahoo.com>

Subj: A002961 No n's == 0 or 5 (mod 6).

Dear seqfans,

Can/wish anybody prove/disprove that, in A002961, there are no terms of 
6*k or 6*k+5,
or find counterexamples
(such n's if any should be ~> 3*10^10).

Thanks, Zak

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