Finite sum of floor function.

Asked Jan 16 '15 at 14:29

Active Jan 16 '15 at 14:29

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Suppose I have the following finite sum;

$$S_n=\sum_{k=1}^n{\left\lfloor{\frac{n}{k}}\right\rfloor}$$ I've never dealt with something like this before and was curious of a way to express it with a closed form. I can see the first few sums are

$$S_1=1$$ $$S_2=2+1=3$$ $$S_3=3+1+1=5$$ $$S_4=4+2+1+1=8$$ $$S_5=5+2+1+1+1=10$$

asked Jan 16 '15 at 14:29

Eleven-Eleven

8,917

See here. – sciona Jan 16 '15 at 14:32
Very interesting... – Eleven-Eleven Jan 16 '15 at 14:35
You can see here http://math.stackexchange.com/questions/740442/how-do-i-evaluate-this-suminvolving-the-floor-function – user207950 Jan 16 '15 at 14:44
That's the same link as @sciona's. Thank you though. – Eleven-Eleven Jan 16 '15 at 14:45

Finite sum of floor function.

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