Summation involving totient function: $\sum_{d\mid n} \varphi(d)=n$
4512
Is there a direct, elementary proof of $n = \sum_{k|n} \phi(k)$?
33104
Combinatorial Proof with Summation Identity
1712
$ d_1,d_2\mid n\iff {\rm lcm}(d_1,d_2)\mid n\ $ [LCM Universal Property]
150092
Iterated sums and asymptotics
35712
Solve for n: $\varphi(2n)=\varphi(3n)$
53116
How find this sum $f(n)=\sum_{i=1}^{n}\dfrac{\binom{n}{i}}{i}$
125148
Summation of series $\sum_{k=0}^\infty 2^k/\binom{2k+1}{k}$
120292
How to formally prove: if $d\mid da+b$, then $d\mid b$?
60031
Showing $\sum\limits_{j=0}^M \frac{M \choose j}{N+M \choose j} = \frac{N+M+1}{N+1}$
62504
Is there any known relationship between $\sum_{i=1}^{n} f(i)$ and $\sum_{i=1}^{n} \dfrac {1}{f(i)}$
91081
Prove that, for every natural n, $\sum_{d|n} \frac{\mu(d)}{d}=\prod_{p|n}(1-\frac{1}{p})$
68481
Finite Summation of Fractional Factorial Series
130945
Summation using residues
71797
Combinatorial argument for $\sum\limits_{k=i}^{n}\binom{n}{k}\binom{k}{i} = \binom{n}{i}2^{n-i}$
151384
Summation of series involving binomial coefficients and polynomial of degree at most n-1
59260
How to prove the convergence of $\sum_{n\geq 0}\frac{n!^d}{(dn)!}$ for $d\geq 2$?
110975
Summation of reciprocals