The inverse zeta function with argument 1, has in terms factors containing primes, the same expression as the Euler function counting the numbers relatively prime to n,, from 1 to n, in terms of the prime factors contained in n, without repetition, as if n could be extrapolated to infinity, and contained all primes.

The expression is

(p1-1)/p1 (p2-1)/p2 ........

disregarding a factor of n in the case of the euler function.

Is this an accident, a coincidence, or is there something to it?