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On the series $ \displaystyle \sum_{n=1}^{\infty} \frac{\Lambda(n)}{\sqrt{n}} \cos(x \log(n) + a) $.

Is the following series ‘summable’ in the sense that it may be divergent but we can attach a meaning to it? $$ \sum_{n=1}^{\infty} \frac{\Lambda(n)}{\sqrt{n}} \cos(x \log(n) + a) = (\text{reg}) ...