When product sigma(k)/d(k) = integer

[Leroy Quet]

I wrote in response to Jack Brennen's observation that the only values 
which are not integer occur when n= 2 or 10, for n < 5000:

>Hmmmm....the question occurs to me and to most probably to others on the 
>list, is the sequence of n's where the product to n is not an integer a 
>finite sequence?
>And if so, what is the top n? Is it 10?

*Proving* the rest of the values of
product{k=1 to n} sigma(k)/d(k)
are integers seems like it might be a tricky problem.

I guess I should post that

product{k=1 to n} sigma(k)/d(k)

=

product{p=primes} product{k>=1}
  ((p^(k+1)-1)/((p-1)(k+1)))^(floor(n/p^k)-floor(n/p^(k+1)))

=

product{p=primes} product{k>=1} ((p^(k+1)-1)*k/((p^k 
-1)(k+1)))^floor(n/p^k).

Maybe this will lead someone to a proof that values of the product for 
all n above n=10 are integers.
Or maybe not.

thanks,
Leroy Quet