# Possibly interesting sequence

David Wilson dwilson at gambitcomm.com
Mon Aug 11 19:29:25 CEST 2008

```So maybe it's best to include the (finite) sequence of "bad" integers,
if not already in the OEIS.

Also, if a sequence is created or annotated, for heaven sakes, don't
call them "Wilson's good numbers". I use the characterization "good
numbers" as shorthand for "numbers that interest me with respect to the
current problem". And in this case, I lifted the problem from another
source, and I have nothing of merit to add to the problem except an
interest in the solution and too much laziness to find it for myself.

Max Alekseyev wrote:
> All integers starting with 78 are good as proved by Graham:
> http://www.math.ucsd.edu/~fan/ron/papers/63_02_partitions.pdf
>
> For integers below 78, it is easy to do exhaustive search to verify
> whether they are good.
>
> Regards,
> Max
>
> On Mon, Aug 11, 2008 at 7:01 AM, David Wilson <dwilson at gambitcomm.com> wrote:
>
>> I found a puzzle site that poses in effect the following problem:
>>
>> For a set S of positive integers, call n = SUM(k in S, k) good when SUM(k in
>> S, 1/k) = 1. Which integers are good?
>>
>> Fun for you programmers.
>>
>>
>>
>
>
>

At 1:32 PM -0400 8/11/08, David Wilson wrote:
>So maybe it's best to include the (finite) sequence of "bad" integers,
>if not already in the OEIS.
>
>Also, if a sequence is created or annotated, for heaven sakes, don't
>call them "Wilson's good numbers". I use the characterization "good
>numbers" as shorthand for "numbers that interest me with respect to the
>current problem". And in this case, I lifted the problem from another
>source, and I have nothing of merit to add to the problem except an
>interest in the solution and too much laziness to find it for myself.
>
>
>Max Alekseyev wrote:
>> All integers starting with 78 are good as proved by Graham:
>> http://www.math.ucsd.edu/~fan/ron/papers/63_02_partitions.pdf
>>
>> For integers below 78, it is easy to do exhaustive search to verify
>> whether they are good.

See A028229

Tony

```