How do I prove$$\lim_{n\to\infty} \sum\limits_{k=1}^n \frac{\Lambda(k)}{k}-\ln(n)=-\gamma $$
Where $\Lambda(k)$ is the Von-Mangoldt function, and gamma is the euler gamma constant
How do I prove$$\lim_{n\to\infty} \sum\limits_{k=1}^n \frac{\Lambda(k)}{k}-\ln(n)=-\gamma $$
Where $\Lambda(k)$ is the Von-Mangoldt function, and gamma is the euler gamma constant