All Questions
4
questions
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163
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On prime-perfect numbers and the equation $\frac{\varphi(n)}{n}=\frac{\varphi(\operatorname{rad}(n))}{\operatorname{rad}(\sigma(n))}$
While I was exploring equations involving multiple compositions of number theoretic functions that satisfy the sequence of even perfect numbers, I wondered next question (below in the Appendix I add a ...
user243301
2
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1
answer
68
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On miscellaneous questions about perfect numbers II
Let $\varphi(m)$ the Euler's totient function and $\sigma(m)$ the sum of divisors function. We also denote the product of primes dividing an integer $m>1$ as $\operatorname{rad}(m)$, that is the ...
user243301
2
votes
1
answer
162
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On even integers $n\geq 2$ satisfying $\varphi(n+1)\leq\frac{\varphi(n)+\varphi(n+2)}{2}$, where $\varphi(m)$ is the Euler's totient
This afternoon I am trying to get variations of sequences inspired from the inequality that defines the so-called strong primes, see the definition of this inequality in number theory from this ...
user243301
2
votes
1
answer
105
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Square-free integers in the sequence $\lambda+\prod_{k=1}^n(\varphi(k)+1)$, where $\lambda\neq 0$ is integer
While I was exploring the squares in the sequence defined for integers $n\geq 1$
$$\prod_{k=1}^n(\varphi(k)+1),\tag{1}$$
where $\varphi(m)$ denotes the Euler's totient function I wondered a different ...
user243301