Where can I find this "generalization" of Ramanujan?

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I read at Wikipedia that

In his notebooks, Ramanujan generalized the Euler product for the zeta function as $\prod_p(x-p^{-s})\approx\frac{1}{Li_s(x)}$

I can also see that Wikipedia mentions at the references Ramanujan's Lost Notebook: Part I, but this seems irrelevant, as Ramanujan deals with continued fractions mostly there. Also after I searched notebook part I, for "zeta function" I found three or four results which do not mention at all $\prod_p(x-p^{-s})\approx\frac{1}{Li_s(x)}$ (or anything similar).
I was wondering if anybody could help me find this "generalization". Is it in another notebook?