Time for some induction

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

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

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