Formula:8722

Digital Library of Mathematical Functions ID 27.5.E5

${\displaystyle{\displaystyle\ln n=\sum_{d\mathbin{|}n}\Lambda\left(d\right)\Longleftrightarrow\Lambda\left(n\right)=\sum_{d\mathbin{|}n}(\ln d)\mu\left(\frac{n}{d}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\Lambda\left(\NVar{n}\right)}}$: Mangoldt’s function
• ${\displaystyle{\displaystyle\mu\left(\NVar{n}\right)}}$: Möbius function
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle d}}$: positive integer
• ${\displaystyle{\displaystyle n}}$: positive integer
 

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