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Tagged with divisors-multiples computational-number-theory
3 questions
69
votes
1
answer
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Iterations of $2^{n-1}+5$: the strong law of small numbers, or something bigger?
I've discovered what I believe is a quite remarkable sequence (A318970), defined by
$$n_1 = 3,\qquad n_{k+1} = 2^{n_k-1}+5\quad(k\geq 1).$$
Here are the first four terms with their prime ...
- 34.4k
3
votes
1
answer
266
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Calculating greatest common divisor series: $\gcd(1,x)+\gcd(2,x)+\gcd(3,x)+....+\gcd(x,x)$ [closed]
How to compute the value of $$[\gcd(1,x)+\gcd(2,x)+\gcd(3,x)+....+\gcd(x,x)]$$ efficiently?
When x can be as large as million.
- 33
0
votes
1
answer
86
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What can be said about $\gcd(N/q^{\alpha},\sigma(N/q^{\alpha}))$ where $N$ is an odd perfect number and $q^{\alpha} \parallel N$?
What can be said about the quantity $$\gcd(N/q^{\alpha},\sigma(N/q^{\alpha}))$$ where $N$ is an odd perfect number and $q^{\alpha} \parallel N$? In particular, can one prove that it is always greater ...
