[seqfan] Re: Two Sequences

[Allan Wechsler]

I think the first proposed sequence is A002805(n) * A007913(A001008(n)).
The contributor has accidentally transposed 6 and 66 in the data, but has
them correct in the derivation.

A001008 gives the numerators of the harmonic numbers; A002805 gives the
denominators; and A007913 provides the factor needed to make the numerator
a square (the squarefree part).

The second sequence is A007947(A001008(n)); A007947 provides the largest
square-free divisor of its argument.

I suspect that the apparent connection to primary Stirling numbers will not
persist.



On Wed, Jul 3, 2019 at 4:19 AM Ali Sada via SeqFan <seqfan at list.seqfan.eu>
wrote:

>
>
>  Hi Everyone,
> I want to suggest the two related sequences below and I would appreciate
> any help and feedback.
>
> I gave the editors a lot of trouble when I added sequences earlier.
> English is not my first language and I am not familiar with many of the
> terms and notations. Also, I use VBA/Excel (based on old knowledge of GW
> BASIC) which is not a good way to present a code for OEIS. For those
> reasons, I would be thankful it if someone could collaborate with me to
> upload these sequences.
> The first sequence is 1, 66, 6, 12, 8220, 20, 420,213080, 17965080,
> 153720, 210951720, 14109480, 31766925960,....
> A(n) is the least integer that when multiplied by the harmonic number sum
> of n generates a square number (M*M.)
> H(1)=1, A(1)=1, M(1)=1
> H(2)=3/2, A(2)=6, M(2)=3 ((6*3/2)^0.5)
> H(3)=11/6, A(3)=66, M(3)=11 ((66*11/6)^0.5)
> H(4)=25/12, A(4)=12, M(4)=5 ((12*25/12)^0.5)
> And so on.
> The second sequence is M itself.
> 1, 3, 11, 5, 137, 7, 33, 761, 7129, 671, 83771, 6617,....
> I searched OEIS and found that this sequence is related to A120299
> (Largest prime factor of Stirling numbers of first kind s(n,2) A000254.)
> A120299 also represents the largest prime factor of M, except for M(1.)
>
> I would really appreciate any feedback and support.
> Best,
> Ali Sada
>
>
>
>
>
>
>
>
>
> --
> Seqfan Mailing list - http://list.seqfan.eu/
>