Let $n$ be a squarefree composite number.
Can $\ \sigma(n)+\varphi(n)\ $ be disivible by $\ n\ $ ?
$\ \varphi(n)\ $ is the totient function and $\ \sigma(n)\ $ the sum of the positive divisors of $\ n\ $.
I solved the case with no more than $\ 3\ $ prime factors. Also, I checked all squarefree numbers without a prime factor exceeding $\ 97\ $. Finally, the OEIS-entries give no example. My conjecture is that there is no such $n$. But how can it be proven ?