You can express it as a summation over Riemann zeta's multiplied by a Möbius function. We have:
where

is the jth prime and the

in the summation range from zero to infinity. Summing over the

gives:
Take the log of both sides:
Expand the logarithm and sum over the primes p:
You can then invert this
relation to find the

using Möbius inversion.