# 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 $$A+B$$.

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