[seqfan] Re: A067081: All terms odd?

[Jack Brennen]

Consider the sequence of n such that:
- n is odd.
- sigma(n) >= 2*sigma(n-1)

It's a very sparse sequence, but has positive density.  If I'm not mistaken,
the first few elements are:

1089250937775
3056930051175
3900221099775


Now replace the >= sign with strict equality.  It gets *really* sparse.
Any even members of the sequence you referenced would
correspond to members of this sequence.


Heuristically, for n which are in the above sequence, the chance
that strict equality occurs is O(1/n).

Since this should behave like a sum of the harmonic series over a
subset of the natural numbers which has positive density,
there should be an infinite number, but finding even one
would appear to be very hard.

On 9/30/2010 10:16 PM, zak seidov wrote:
> A067081: Are all terms odd?
>
> Thanks,
> Zak
>
> %S A067081 5,125,1253,1673,3127
> %N A067081 ...sigma(n+1)=2*sigma(n).
> %C A067081 ...odd values only(?)
>
>
>
>
>
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