Time for some induction

Number Theory Level 5

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

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 \(A+B\).