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Order of magnitude of $\sum \frac{1}{\log^2{p}}$, or $\sum \frac{1}{\log^a{p}}$ for arbitrary power $a$ [closed]
In this MO question, it says that we have
$$ \sum_{p<n} \frac{1}{\log{p}} =\frac{n}{\log^2 n}+O\left(\frac{n\log\log n}{\log^3 n}\right).$$
where the sum is on all primes $p$, up to some max ...
- 4,897
0
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0
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143
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Given $\,m=\prod_k {p_k}^{\alpha_k}\,$ and the function $\,g(m)=\sum_k \alpha_k(p_k-1)^2$, find all solutions of the equation $\,g(2n)=n$
Let's consider the unique decomposition of a natural number $\,m\,$ into its prime factors:
$$\prod_k {p_k}^{\alpha_k}$$
Then, let's define the following arithmetic function (completely additive) $\,g:...
- 1,008
-1
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14
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Priming for the primes [closed]
I have to confess that most often my eyes begin to glaze over when someone starts discussing the prime numbers. However, my ears have perked up at times over the primes--maybe first when I learned of ...
-1
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1
answer
283
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Is it possible to determine whether the sequence $\,a_0=p,\;a_{n+1}=(a_n-2)\cdot a_n+2\,$ will reach another prime number?
Given a prime $\,p\,$ let's consider the following sequence:
$a_0=p$
$a_{n+1}=(a_n-2)\cdot a_n+2$
Is it possible to determine whether the sequence $\,a_n\,$ will reach, sooner or later, another ...
- 1,008