New posts in Divisor Sum

USA TST 2018/P1: Prove that the $n^{\text{th}}$ smallest positive integer relatively prime to $n$ is at least $\sigma(n)$

Why did the Egyptians not represent $2/3$ as a sum of unit fractions in the Rhind papyrus?

The equation $\sigma(n)=\sigma(n+1)$

Any suggestions on a closed form of $\sum_{a=1}^{N} \left({\lfloor{\frac{N+1}{a}}\rfloor+\lfloor{\frac{N-1}{a}}\rfloor}\right)$

Evaluating the sum $\sum_{i=1}^n i^2\cdot\lfloor{\frac ni}\rfloor$

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

Are there any natural numbers $n$ that satisfy the condition $7921\sigma(n) = 15840n$?

A conjecture concerning the number of divisors and the sum of divisors.

$\sigma(n) \equiv 1 \space \pmod{n}$ if and only if $n$ is prime

When $p$ is an odd prime, is $(p+2)/p$ an outlaw or an index?