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

[Farideh Firoozbakht]

Quoting 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


Dear Zak,

I think it isn't true that
" in A002961, there are no terms of forms 6*k or 6*k+5 "
But if 6*k is in the sequence then 6k+1 has a large number
of distinct prime factors so 6*k >> 3*10^10 and it isn't easy to
find it. Also if 6*k+5 is in the sequence then 6k+6 has a large
number of distinct prime factors so 6k+5 >> 3*10^10 and it is
difficult to find it.
In fact it seems that in the range that you have searched we have
sigma(6*k) > sigma(6*k +1) so sigma(6*k) <> sigma(6*k+1) and 6*k
cannot be in the sequence.
Also I think in this range sigma(6*k+6) > sigma(6*k +5) so
sigma(6*k+5) <> sigma(6*k+6) and 6*k+5 cannot be in the sequence.


Best regards,

Farideh









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