Mangoldt

\[\large \dfrac 1{\gamma} \sum\limits_{n=1}^{\infty} \frac{\Lambda(n)-1}{n}= \, ? \]

Notations:

  • \( \gamma\) denotes the Euler–Mascheroni constant, \(\displaystyle\gamma = \lim_{n\to\infty} \left( - \ln(n) + \sum_{k=1}^n \dfrac1k \right) \approx 0.5772 \).

  • \(\Lambda\) denotes the Von Mangoldt function.

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