Hilbert series and Generting functions anyone?

Question

Fix a positive integer n. Let A(n) be the commutative algebra generated by indeterminates xi, for i running over the divisors of n, subject to the relations
xixj = xgcd(i,j)xlcm(i,j)
for all i,j.
Problem: What is the Hilbert series for A(n), the generating function for the sequence whose kth term is the dimension of the space of elements of degree k in the algebra?

Answer 1

Say that again slowly?

Answer 2

i imagine you made a mistake even as using the ratio try. I were given: (-a million)^(n+2)/(n+a million)*(n)/(-a million)^(n+a million) = ((-a million)^(n)*(-a million)^2) /(n+a million))*(n/(-a million)^n*(-a million)^a million) the (-a million)^n cancels and also you're left with n/n+a million = a million/a million = a million desire this enables Yeah you're precise notwithstanding absolutely the cost indicators on the proper set it equivalent to +a million