Doing some calculations concerning relative Merten's function I found quite interesting form of the Zeta function formula which is actually the specific rearrangement of the infinite Euler’s product into combination of Sum of products.
To make it easier, let’s name:
So:
And it can be written in such a new form – a sum of finite products:
It also has these properties that:
This way of reformulation works also for natural numbers (2, inf.) but applied to primes looks much more interesting :-).
I haven't found a use for it yet, but maybe there is some? :-)
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