# Tagged Questions

For questions on arithmetic functions, a real or complex valued function $f(n)$ defined on the set of natural numbers.

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### Counting divisors of a number

Let m be any positive integer and consider $\Sigma_{d|m} \frac{1}{d}$. I wish to ask whether there is a closed form expression for the above sum.
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### Using Dirichlet convolution where f = μ ∗ μ (Mobius) to find f(24)?

I am confused about the Dirichlet convolution and how it is used. Does it take two entirely different arithmetic functions? And knowing that f = μ ∗ μ (the Mobius function), why does the question I ...
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### Infinite sum of a function $g(n)=\sum_{d|n \; d\ne n}g(d)$

Let the function $g:\Bbb{N}\to\Bbb{N}$ be defined as $$g(n)=\sum_{d|n \; d\ne n}g(d)$$ with $g(1)=1$, how can we evaluate a sum like $$\sum_{i=0}^\infty{g(15^i)\over15^i} \tag1$$ Need we find a ...
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### Show that if $n$ is even then $\sum_{d|n}\mu(d)\phi(d)=0$ using only Dirichlet Convolution propertys (without multiplicative function concepts)

Show that $\displaystyle\sum_{d|n}\mu(d)\phi(d)=0$ using only Dirichlet Convolution propertys (without multiplicative function concepts). I suspect you have to use that $1\ast \mu=I$ and $f\ast 1=id$...