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New posts in divisor-sum
Does the following lower bound improve on $I(q^k) + I(n^2) > 3 - \frac{q-2}{q(q-1)}$, where $q^k n^2$ is an odd perfect number? - Part II
upper-lower-bounds
conjectures
divisor-sum
arithmetic-functions
perfect-numbers
$\sigma(n) \equiv 1 \space \pmod{n}$ if and only if $n$ is prime
number-theory
prime-numbers
modular-arithmetic
divisor-sum
The sigma function (sum of divisors) multiplicative proof
elementary-number-theory
prime-numbers
divisor-sum
multiplicative-function
An integer is prime iff $\phi(n) \mid n-1$ and $n+1 \mid \sigma (n)$
divisibility
totient-function
divisor-sum
elementary-number-theory
Can this bound for the abundancy index of $n$ be improved, given that $q^k n^2$ is an odd perfect number with $k=1$?
elementary-number-theory
inequality
conjectures
divisor-sum
perfect-numbers
Proving that $\sigma_7(n) = \sigma_3(n) + 120 \sum_{m=1}^{n-1} \sigma_3(m)\sigma_3(n-m)$ without using modular forms?
number-theory
elementary-number-theory
modular-forms
divisor-sum
Help with "A Simpler Dense Proof regarding the Abundancy Index."
number-theory
divisor-sum
arithmetic-functions
perfect-numbers
The equation $\sigma(n)=\sigma(n+1)$
number-theory
elementary-number-theory
divisor-sum
oeis
On odd perfect numbers and a GCD - Part V
number-theory
solution-verification
gcd-and-lcm
divisor-sum
perfect-numbers
When $p$ is an odd prime, is $(p+2)/p$ an outlaw or an index?
number-theory
elementary-number-theory
conjectures
divisor-sum
perfect-numbers
On odd perfect numbers and a GCD - Part VI
number-theory
solution-verification
gcd-and-lcm
divisor-sum
perfect-numbers
On the conjectured inequality $q > k$, where $q^k n^2$ is an odd perfect number with special prime $q$
number-theory
inequality
upper-lower-bounds
divisor-sum
perfect-numbers
Asymptotic formula for $\sum_{n\leq x}\sigma(n)$ knowing $\sum_{n\leq x}\frac{\sigma(n)}{n}$
asymptotics
analytic-number-theory
divisor-sum
What is the sum of all positive even divisors of 1000?
elementary-number-theory
summation
factoring
divisor-sum
A number $n$ which is the sum of all numbers $k$ with $\sigma(k)=n$?
elementary-number-theory
divisor-sum
experimental-mathematics
Are there any natural numbers $n$ that satisfy the condition $7921\sigma(n) = 15840n$?
group-theory
elementary-number-theory
finite-groups
normal-subgroups
divisor-sum
Does there exist $a_0$, such that $\{a_n\}_{n=0}^{\infty}$ is unbounded?
number-theory
elementary-number-theory
recurrence-relations
totient-function
divisor-sum
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