Time for some induction

Number Theory Level 4

$\large \sum_{k=1}^n \left \lfloor \frac nk \right \rfloor \phi(k)$

Let $\phi$ denote the Euler's Totient Function. If the summation above is equal to $\dfrac{n(n+A)}B$ , where $A$ and $B$ are integers, find the value of $A+B$ .

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