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Arithmetical Functions Sum, $\sum\limits_{d|n}\sigma(d)\phi(\frac{n}{d})$ and $\sum\limits_{d|n}\tau(d)\phi(\frac{n}{d})$

The most peculiar totient sum: $\sum_{n=1}^{\infty} \frac{\phi(n)}{5^n +1}$

Why does $\phi(pq)=\phi(p)\phi(q)$?

Calculating Euler's totient function values.

Problem on Euler's Phi function

If $\varphi(x) = m$ has exactly two solutions is it possible that both solutions are even?

Is there an odd solution of $\varphi(n)+n=\sigma(n)$?

$1 = \phi(\phi(\cdots\phi(n)\cdots))$, where Euler's totient is applied $k$ times, then $n\leq 3^k$

Why is Euler's totient function equal to $(p-1)(q-1)$ when $N=pq$ and $p$ and $q$ are prime in a clean intuitive way?

Why is $\prod_{k = 1}^t p_k^{\alpha_k - 1}(p_k-1) = n \prod_{p\mid n} \left(1 - \frac {1}{p} \right)$?

$n\cdot \phi(n)=m\cdot \phi(m)$

Only finitely many $n$ such that $\phi(n) = m$

Is there a recursive formula for Euler's Totient function

For which natural numbers are $\phi(n)=2$?

New posts in totient-function

Efficient way to compute $\sum_{i=1}^n \varphi(i) $

Euler function and sums

Proof on Euler totient function

Prove that $n$ divides $\phi(a^n-1)$, where $\phi$ is Euler's $\phi$-function.

The number of summands $\phi(n)$

Can a composite number $n$ be the arithmetic mean of $\sigma(n)$ and $\varphi(n)$?

Arithmetical Functions Sum, $\sum\limits_{d|n}\sigma(d)\phi(\frac{n}{d})$ and $\sum\limits_{d|n}\tau(d)\phi(\frac{n}{d})$

The most peculiar totient sum: $\sum_{n=1}^{\infty} \frac{\phi(n)}{5^n +1}$

Why does $\phi(pq)=\phi(p)\phi(q)$?

Calculating Euler's totient function values.

Problem on Euler's Phi function

If $\varphi(x) = m$ has exactly two solutions is it possible that both solutions are even?

Is there an odd solution of $\varphi(n)+n=\sigma(n)$?

$1 = \phi(\phi(\cdots\phi(n)\cdots))$, where Euler's totient is applied $k$ times, then $n\leq 3^k$

Why is Euler's totient function equal to $(p-1)(q-1)$ when $N=pq$ and $p$ and $q$ are prime in a clean intuitive way?

Why is $\prod_{k = 1}^t p_k^{\alpha_k - 1}(p_k-1) = n \prod_{p\mid n} \left(1 - \frac {1}{p} \right)$?

$n\cdot \phi(n)=m\cdot \phi(m)$

Only finitely many $n$ such that $\phi(n) = m$

Is there a recursive formula for Euler's Totient function

For which natural numbers are $\phi(n)=2$?