[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
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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