[seqfan] Re: Two Sequences

[Ali Sada]

 Hi Allan,
Thank you very much for your response. And I am sorry about the typo. 

Regarding your notes, and I am not fully aware of OEIS rules, would that make the sequences I suggested unacceptable? 

As for the connection to primary Stirling numbers, Excel didn't work well after few numbers. It starts decimal approximation after 10^10. I would really appreciate it if you or any other Seqfan friend could check this with better programs. In my opinion, I think it's highly improbable that the connection to primary Stirling numbers will change.
Best,
Ali 

    On Wednesday, July 3, 2019, 8:55:07 AM EDT, Allan Wechsler <acwacw at gmail.com> wrote:  
 
 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 









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