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Results tagged with nt.number-theory
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user 40984
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
3
votes
1
answer
625
views
Is anything like $\phi(n)>\dfrac n{e^\gamma\log\log n},\ \sigma(n)<e^\gamma n\log\log n$ kno...
Is anything like $\dfrac n{\phi(n)}<\dfrac{\sigma(n)}n<e^\gamma\log\log n$ known/conjectured for the generalizations of these functions?
Let $n=p_1^{a_1}\cdots p_t^{a_t}$ be the canonical prime facto …
- 205
2
votes
0
answers
221
views
Determine whether if $n$ is a primitive pseudoperfect (semiperfect) number, then $\sigma(n)<...
Determine whether if $n$ is a primitive pseudoperfect (semiperfect) number, then $\sigma(n)<2^{\sigma_0(n)}$.
$\sigma_k(n)$ is the division function and $\sigma(n)=\sigma_1(n)$. A number is called p …
- 205
3
votes
Interactions of number theoretic conjectures and other fields of mathematics
This is an elaboration of a now deleted comment, written at the request of OP. I've had a couple of conjectures published on the OEIS which I really think justify some obvious numerical observations o …
5
votes
1
answer
601
views
Who is attributed with the conjecture that every multiply-perfect number greater than $1$ is...
I know that Descartes is considered to be the first to ask whether or not odd perfect numbers exist ($n$ such that $\sigma(n)=2n$, where $\sigma(n)$ is the sum of divisors of $n$), and he also discove …
- 205