Consider the algebraic definition of Von Mangoldt function as follows: $\Lambda(f) = deg P$ if $f= cP^k$ is a power of a prime P($k\geq 1$) and is 0 otherwise.
$\sum_{P prime} deg(P) \sum_{m=1} u^{m deg P} = \sum_{f Monic} \Lambda(f) u^{deg f}$.
As , deg(P) = $\Lambda(f) $ so I can see easily how it is used in deg(P) =$\Lambda(f) $, but I am unable to see how $\sum_{m=1}^{\infty} u^{m deg P} = u^{deg f}$ .
Can you please help.