> Are there infinitely many postive integers $\ n\ $ satisfying $$\varphi(n)\mid \sigma(n)$$ where $\varphi(n)$ is Euler’s totient function, and $\sigma(n)$ is the sum of divisors of $n$? If yes, can it be proven? The first few such $\ n\ $ are $$n=1, 2, 3, 6, 12, 14, 15, 30, 35, 42, 56, 70, 78, 105, 140, 168, 190.$$ Ideas for a proof of the existence of infinitely many such positive integers (like families of such numbers probably being infinite) are appreciated. I posted this question to Math.StackExchange, but I couldn't get reaction. That is why I'm asking this here. If this is not suitable for this place, please answer at Math.StackExchange: [Are there infinite many positive integers $\ n\ $ satisfying $\ \varphi(n)|\sigma(n)\ $?](https://math.stackexchange.com/questions/4407570/are-there-infinite-many-positive-integers-n-satisfying-varphin-sigm)