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Mangoldt function

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1: 27.2 Functions
27.2.14 Λ ( n ) = ln p , n = p a ,
This is Mangoldt’s function. …
2: 27.5 Inversion Formulas
27.5.5 ln n = d | n Λ ( d ) Λ ( n ) = d | n ( ln d ) μ ( n d ) .
3: 27.4 Euler Products and Dirichlet Series
27.4.12 n = 1 Λ ( n ) n - s = - ζ ( s ) ζ ( s ) , s > 1 ,
4: 27.3 Multiplicative Properties
Except for ν ( n ) , Λ ( n ) , p n , and π ( x ) , the functions in §27.2 are multiplicative, which means f ( 1 ) = 1 and …