computation of sum with primes
Can anyone tell me the value of sum using mathematica. \sum_p\left(\log
p(\frac{1}{2p}-\psi(\frac{p+2}{2})+\psi(\frac{p+1}{2})\right)-\sum_n\frac{(\log(2^n)}{2^n}
where p ranges over prime powers and n ranges from 1 to infinity. ø is the
digamma function . I tried but didnot got the answer
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