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Wikipedia has a page about the prime zeta function which is defined as follows:

$P(s)=\sum_{p\;\text{prime}} \frac1{p^s}$

I entered this additional definition:

Define a sequence: $a_n=\prod_{d\mid n} \frac{\Lambda(d)}{\log(d)},$ where zeros are not included in the multiplication and $a_1=1$ then: $P(s)=\log\sum_{n=1}^\infty \frac{a_n}{n^s}.$ Is it a problem that this later definition does not include the zeros in the multiplication?

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    If you add a new definition to Wikipedia, please have a reference for it, preferably in the form of a published article.2018-12-17

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