Pillai's arithmetical function

In number theory, the gcd-sum function, also called Pillai's arithmetical function, is defined for every ${\displaystyle n}$ by

or equivalently

where ${\displaystyle d}$ is a divisor of ${\displaystyle n}$ and ${\displaystyle \varphi }$ is Euler's totient function.

it also can be written as

...
Wikipedia