BDHPS conjecture for the Euler totient partial sum

Let

be the Euler totient function, and for real $x\to$ define

S_{\varphi}(x):=\sum_{n\leq x}\varphi\left(\left\lfloor x/n \right\rfloor\right).

$$**BDHPS conjecture.**$$

S_{\varphi}(x)=\dfrac{x\log(x)}{\zeta(2)}(1+o(1)).

$$Here$$

denotes the Riemann zeta function. The conjecture predicts an asymptotic formula for this variant of the classical summatory Euler totient function; the source reports that it arose from numerical evidence, while the status is not established by the supplied text.