math.CO/0409509 number 17

[rwst]

What is the conjecture

$$ \begin{multline}\left(\binom{2n}{n},\binom{3n}{n},\dotsc,\binom{(n-1)n}{n}\right)=1 \iff \\ n+1=\sum_ip_i^{e_i} \wedge m = \max_ip_i^{e_i} \wedge \frac{n+1}{m} > m.\end{multline} $$

See also https://oeis.org/A080170 and https://oeis.org/A051283

Prerequisites needed

Status: open

Choose either option

• I plan on adding this conjecture to the repository
• This issue is up for grabs: I would like to see this conjecture added by somebody else

[Aditi0522]

Hello @rwst
I would like to work on this issue if it's available. I’ve reviewed the conjecture and the referenced OEIS sequences (A080170 and A051283), and I understand the intended connection. I can work on properly formalizing and adding the conjecture to the repository in line with existing conventions.

Let me know if that works — thanks!

[rwst]

Please go ahead. I don't have the rights to assign anyone at the moment but it should be clear from this thread.

[Aditi0522]

Thanks! I’ll start working on the PR and will link it here once ready.