List questions from arithmetic-functions | MathQa

Arithmetic Derivative

Published on 12 Jan 2025 - 17:23

Formula with $\sigma(n)$ and $\phi(n)$ is not an integer if $n$ is not square-free

Published on 12 Jan 2025 - 9:10

The sum $\sum_{n\leq x}\sum_{\substack{1\leq k\leq n \\ gdc(k,n)=1}}\cos^2\pi \frac{k}{n}$ diverges as $x$, when $x$ tends to infitity

Published on 12 Jan 2025 - 23:35

On $\sigma(n)<n+\frac{n}{2}\log\frac{n+1}{n-1}+\frac{n}{4} \left(\sum_{\substack{d|n,1<d<n}}\log\frac{(n+d)(n+1)}{(n-d)(n-1)}\right)$

Published on 12 Jan 2025 - 23:39

Numbers $n$ whose prime factors are $2$ and $5$ if and only if $\sum_{k=1}^{rad(n)}\mu(k)k=0$?

Published on 28 Dec 2024 - 9:57

Show that if $n$ is even then $\sum_{d|n}\mu(d)\phi(d)=0$ using only Dirichlet Convolution propertys (without multiplicative function concepts)

Published on 12 Jan 2025 - 9:10

Infinite sum of a function $g(n)=\sum_{d|n \; d\ne n}g(d)$

Published on 12 Jan 2025 - 23:32

Using Dirichlet convolution where f = μ ∗ μ (Mobius) to find f(24)?

Published on 12 Jan 2025 - 23:30

Counting divisors of a number

Published on 12 Jan 2025 - 18:31

With $s(n)=\sum_{k=1}^n n \bmod k$, can be justified that $\forall\epsilon>0$ let us $\lim_{n\to\infty}\frac{s(n-1)}{\epsilon+s(n)}=1?$

Published on 02 Jan 2025 - 16:53