consider the arithmetic function
Read dirichlet convolution and dirichlet series . we have
This is because disappears over non-primes. Consider the case
n is square free.then and when we add over all prime factors we get .
Not squarefree but only one prime factor is squared. then it's möbius will be zero everywhere except the repeated prime factor. so we get .
more than one prime factor is squared. then it will simply be zero.
I will continue this in part 2. Reshare if you enjoyed this.
btw is the nmber of prime factors of n and is the möbius function