[seqfan] Re: A sequence and a related array

[Olivier Gerard]

The sequence you are looking for is
"Kempner Numbers", A002034

1, 2, 3, 4, 5, 3, 7, 4, 6, 5, 11, 4, 13, 7, 5, 6, 17, 6, 19, 5, 7, ...

Olivier Gérard


On Sun, Jul 4, 2021 at 10:15 AM Ali Sada via SeqFan <seqfan at list.seqfan.eu>
wrote:

> Hi everyone,
>
> If we want to make sure that we have a multiple of a certain positive
> integer n we can simply multiply n consecutive integers. For example,
> multiplying 11 consecutive numbers will certainly give us a multiple of 11.
> However, some numbers don’t need n terms to get that multiple. For
> example, we can get a multiple of 6 by multiplying only three integers
> m(m+1)(m+2), which means that a(6) = 3. Or if we want a multiple of 7 we
> need only five terms m(m+1) (m-1)(m^2+m+1)(m^2-m+1). So, what is the least
> number of these non-factor-able terms we need to multiply in order to get a
> multiple of n? I would really appreciate your help with this sequence if
> you thought it’s suitable for the OEIS.
>
> The related array is “the largest common factor of m^k-m^n, where m > 1, n
> = 1,2,3,.., and k > n."
> For example, the largest common factor of m^8-m^2 is 252. I would
> appreciate your help with this one too.
>
> Best,
>
> Ali
>
>
>
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