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Apologies in advance for the simplicity of the question, but I can't fathom how to write the following as a sum in Mathemaitca:

\begin{align} &\sum_{p}^{a}\sum_{n}^{b}\text{expression} \end{align}

where $p$ runs through the primes.

I would like to plot

\begin{align} &\sum_{p}^{a}\sum_{n}^{b}(1/n)p^{-ns} \end{align}

in $s$ for some $a,b$.

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  • $\begingroup$ @Kuba thankyou very much - I think I haven't quite woken up yet! ;) $\endgroup$ – martin Mar 2 '15 at 11:10
  • $\begingroup$ @kuba - should I delete? $\endgroup$ – martin Mar 2 '15 at 11:11
  • $\begingroup$ I don't think so. Not bad question. I felt like it is a dupe but I've faile to find one. Let me post an answer. $\endgroup$ – Kuba Mar 2 '15 at 11:13
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    $\begingroup$ related: 52371 $\endgroup$ – Kuba Mar 2 '15 at 11:17
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I think this is what you are after:

 mySum[s_, a_, b_]:= Sum[  1./n p^(-n s), 
                           {n, b},  
                           {p, Prime @ Range @ PrimePi @ a}]

Edit: skipper inner Sum, thanks to kguler's comment.

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    $\begingroup$ Simpler: Sum[1/n p^(-n s), {n, b}, {p, Prime@Range@PrimePi@a}] (+1) $\endgroup$ – kglr Mar 2 '15 at 13:34

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