I am considering the product V\sub{n,m}(Q)=\prod\sub{i=Q+1}^{Q+m} (1-[1/(i,p\sub{n}\#)]) and the sum over this product S\sub n(m)=\sum\sub{i=0}^{p\sub{n}\#-1} V\sub{n,m}(i).

In particular, I have found that S\sub n(2m+2)-S\sub n(2m+1)=S\sub n(2m+1)-S\sub n(2m), and I am looking for similar identities for multiples of $m$ that are larger than 2.

Edit: not sure how it might translate, but it would be nice to be able to use MathJAX here.