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

[zak seidov]

--- On Tue, 1/5/10, franktaw at netscape.net <franktaw at netscape.net> wrote:

> From: franktaw at netscape.net <franktaw at netscape.net>
> Subject: [seqfan] Re: A002961: sigma(n)=sigma(n+1).
> To: seqfan at list.seqfan.eu
> Date: Tuesday, January 5, 2010, 3:22 PM
> I'm not sure where you got your
> 3*10^10 number (the b-file goes to 
> 2*10^10).  

Seven last terms (calc'd by me) are: 
1598, 30946497741
1599, 31007605214 
1600, 31026742929
1601, 31048568005
1602, 31113186542
1603, 31257726338
1604, 31411356404

>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 
> forms
> 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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