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Tagged with prime-factorization sequences-and-series
4
questions
13
votes
1
answer
344
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Prime divisors of the sequence terms $a_n=a\cdot 2017^n+b\cdot 2016^n$
I am dealing with the test of the OBM (Brasilian Math Olimpyad), University level, 2017, phase 2.
As I've said at another topic (question 1), I hope someone can help me to discuss this test.
The ...
- 1,525
2
votes
1
answer
203
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Do we know the rate of divergence of the sum of reciprocals of the $k$-almost primes?
A $k$-almost prime is a positive integer having exactly $k$ prime factors, not necessarily distinct. Let $\mathbb{P}_k$ be the set of the $k$-almost primes and let $$ \rho_k(n):=\sum\limits_{\substack{...
- 7,299
4
votes
1
answer
194
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Sequence generated by $2^k-1$ contains new prime factors
I was playing around with the sequence where the $k^{th}$ number is equal to $2^k-1$. It seems that all numbers except $63$ contain at least one new prime in there prime factorization. That is a prime ...
- 2,086
-2
votes
1
answer
107
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On an inequality involving the radical of an integer and its greatest prime factor
Let $n\geq 1$ an integer, in this post I denote the greatest prime dividing $n$ as $\operatorname{gpf}(n)$, and the product of the distinct prime numbers dividing $n$ as $$\operatorname{rad}(n)=\prod_{...
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