Tagged Questions
7
votes
2answers
98 views
Efficient computation of $\sum_{k=1}^n \lfloor \frac{n}{k}\rfloor$
I realize there is probably not a closed form, but is there an efficient way to calculate the following expression?
$$\sum_{k=1}^n \left\lfloor \frac{n}{k}\right\rfloor$$
I've noticed $$\sum_{k=1}^n ...
1
vote
1answer
46 views
How are 10-20 digit multiperfect and hemiperfect numbers efficiently computed?
This numericana item on multiperfect and hemiperfect numbers contains some impressively enormous numbers. How were these actually computed ? The associated OEIS pages (A007691 & A159907) just ...
1
vote
1answer
33 views
Amicable numbers
Def: a pair natural numbers $a$, $b$, $a\ne b$ are an Amicable pair if
$\sum_{d|a,a\ne d}d = b$ and $\sum_{d|b, b\ne d}d = a$.
Ok. So I'm trying to optimize a calculation for finding the number of ...
1
vote
1answer
120 views
Can someone explain to me the relationship between primorials and factorials and how that relation can be used to compute large factorials?
What I am trying to figure out is a way to compute large factorials, !1000000.
For what it's worth luschny's computer algorithms do a very good job of it.
2
votes
0answers
160 views
Optimal division sequences for divide-and-conquer algorithms
Say we have a discrete data set of some size, and we can use a recursive divide-and-conquer algorithm to process the data in some way (an FFT for example). The naive solution is, say, $n^2$ in ...
