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Tagged with prime-factorization totient-function
6
questions with no upvoted or accepted answers
8
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Odd numbers with $\varphi(n)/n < 1/2$
The topic was also discussed in this MathOverflow question.
From $\varphi(n)/n = \prod_{p|n}(1-1/p)$ (Euler's product formula) one concludes that even numbers $n$ must have $\varphi(n)/n \leq 1/2$ ...
- 18.2k
6
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Estimation of the number of solutions for the equation $\sigma(\varphi(n))=\sigma(\operatorname{rad}(n))$
For integers $n\geq 1$ in this post we denote the square-free kernel as $$\operatorname{rad}(n)=\prod_{\substack{p\mid n\\p\text{ prime}}}p,$$ that is the product of distinct primes dividing an ...
user243301
3
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An integer sequence defined from a variation of the Lucas–Lehmer primality test: the case of the Euler's totient function
I did a variation of the so-called Lucas–Lehmer primality test,
I say this Wikipedia. I've used the Euler's totient function
$$\varphi(n)=n\prod_{\substack{p\mid n\\ p\text{ prime}}}\left(1-\frac{1}{...
user243301
2
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68
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Largest possible prime factor for given $k$?
Let $k$ be a positive integer.
What is the largest possible prime factor of a squarefree positive integer $\ n\ $ with $\ \omega(n)=k\ $ (That is, it has exactly $\ k\ $ prime factors) satisfying the ...
- 85.1k
2
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On variations of Erdős squarefree conjecture: presentation and a question as a simple case
I'm inspired in the so-called Erdős squarefree conjecture, this section from Wikipedia, to state in this post a question, involving a different arithmetic function, that due its difficulty I feel as ...
user243301
1
vote
0
answers
801
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number of coprimes to a less than b
We know that number of coprimes less than a number can be found using euler function https://brilliant.org/wiki/eulers-totient-function/ But if there are two numbers p,q and we need to find number of ...
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