Difference between revisions of "Relationship between logarithm and Mangoldt"
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(Created page with "==Theorem== The following formula holds: $$\log(n) = \displaystyle\sum_{d | n} \Lambda(d),$$ where $\log$ denotes the natural logarithm and the notation $d | n$...") |
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The following formula holds: | The following formula holds: | ||
$$\log(n) = \displaystyle\sum_{d | n} \Lambda(d),$$ | $$\log(n) = \displaystyle\sum_{d | n} \Lambda(d),$$ | ||
| − | where $\log$ denotes the [[ | + | where $\log$ denotes the [[logarithm]], the notation $d | n$ denotes that $d$ is a [[divisor]] of $n$, and $\Lambda$ denotes the [[Mangoldt]] function. |
==Proof== | ==Proof== | ||
Latest revision as of 16:31, 16 June 2016
Theorem
The following formula holds: $$\log(n) = \displaystyle\sum_{d | n} \Lambda(d),$$ where $\log$ denotes the logarithm, the notation $d | n$ denotes that $d$ is a divisor of $n$, and $\Lambda$ denotes the Mangoldt function.
