[seqfan] Re: Comment on A151750 [erratum]

[David Wilson]

> Thank you David. When reading your proof Legendre's theorem and
> Kummer's theorem comes to my mind. I think Andrew Granville
> has given a nice exposition on that somewhere on the web.
> But why restrict oneself to the case choose(2n,n)? I will
> recast the theorem in terms of the swinging factorial n$.
> 
> Theorem: For prime p
> 
>   p does not divide n$ <=> exists k such [n/p^k] is odd.
> 
> Proof: The exponent of prime p in n$ is given by
> 
>   e_p(n) = sum{k>0} [n/p^k] mod 2 .

Not true, methinks.

> 
> QED.

e_p(n) = sum{k>0} [n/p^k] mod 2