Today I suddenly discovered that many positive integers $\ n\ $ satisfy $\ \varphi(n)\mid \sigma(n)\ $. This leads to the following question :
Are there infinitely many postive integers $\ n\ $ satisfying $$\varphi(n)|\sigma(n)$$ 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 infinite many such positive integers (like families of such numbers probably being infinite) are appreciated.