For the repeated calculation \ ({\ biggl \ lfloor \ frac {k} {n} \ biggr \ rfloor} \) problems, as a result of monotone, and repeated the same number can be divided into stages, simplified calculation.
Example: Calculation
\[\sum_{i=1}^{n}k\mod i\]
Be turned into
\[nk-\sum_{i=1}^{n}i{\biggl\lfloor\frac{k}{i}\biggr\rfloor}\]
Consider the nature of (the core can be rote
\[{\biggl\lfloor\frac{k}{{\bigl\lfloor\frac{k}{{\bigl\lfloor\frac{k}{i}\bigr\rfloor}}\bigr\rfloor}}\biggr\rfloor}={\biggl\lfloor\frac{k}{i}\biggr\rfloor}\]
Order \ [{{\ biggl \ lfloor \ frac {k} {{\ bigl \ lfloor \ frac {k} {i} \ bigr \ rfloor}} \ biggr \ rfloor}} = g (i) \] every time can be calculated
\[i\sum_{j=g(i-1)+1}^{g(i)}j\]
Use arithmetic sequence summation formula can be.
(To be continued)