[seqfan] Re: FW: A100083

[Max Alekseyev]

If exists, a(17) is be prime.
It cannot be a nontrivial prime power as otherwise smaller powers of
the same prime would be in the sequence, while 2^4, 31^2, and 373^2
are not terms of this sequence.
Max

On Tue, Jun 11, 2013 at 7:36 PM, Robert Gerbicz
<robert.gerbicz at gmail.com> wrote:
> My submitted comment: If n is in the sequence and k|n then k is also in the
> sequence. In the other direction if s and t is in the sequence and
> gcd(s,t)=1 then n=s*t is also in the sequence. This gives that we need to
> check only the primepowers, then we can easily build the rest of the
> sequence. The primepowers in the sequence begins with: 2,4,8,31,373
>
> ps. This can also speedup a naive search.
>
>
> 2013/6/11 Giovanni Resta <g.resta at iit.cnr.it>
>
>> On 06/11/2013 09:33 PM, Harvey P. Dale wrote:
>>
>>>  That might suggest that the next term of the "reduced series" is
>>>
>> either 4312999 (373 x 11563) or
>> > perhaps 133702969 (31 x 373 x 11563).
>>
>> I've not reached these two values (I'm just at 3.3*10^6 and the program
>> becomes slower and slower), but I've checked them directly and they do not
>> seem to belong to the sequence.
>>
>> Giovanni
>>
>>
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