All Questions
3
questions
5
votes
2
answers
194
views
Periodic sequences of integers generated by $a_{n+1}=\operatorname{rad}(a_{n})+\operatorname{rad}(a_{n-1})$
Let's define the radical of the positive integer $n$ as
$$\operatorname{rad}(n)=\prod_{\substack{p\mid n\\ p\text{ prime}}}p$$
and consider the following Fibonacci-like sequence
$$a_{n+1}=\...
- 1,828
5
votes
1
answer
135
views
What about sequences $\{\sum_{k=1}^n (\operatorname{rad}(k))^p\}_{n\geq 1}$ containing an infinitude of prime numbers, where $p\geq 1$ is integer?
We denote the radical of the integer $n> 1$ as
$$\operatorname{rad}(n)=\prod_{\substack{p\mid n\\ p\text{ prime}}}p,$$
taking $\operatorname{rad}(1)=1$ that is this definition from Wikipedia.
In ...
user243301
0
votes
2
answers
72
views
On variations of Rowland's sequence using the radical of an integer $\prod_{p\mid n}p$
This afternoon I tried to create a Rowland's sequence using the radical of an integer in my formula. I don't know if it was in the literature, but I know that also there were variations on Rowland's ...
user243301