Let $\sigma(n)$ be the sum of all divisors of $n$ (including $1$ and $n$). Is this function, $$f(x)=(e^\gamma(n+1))\ln(\ln n)+\ln(e^\gamma n)$$ an upper bound of $\sigma(n)$ for sufficiently large $n$? If so, how large must $n$ be to be "sufficiently large"?
2026-03-25 17:19:54.1774459194
Possible Upper Bound of Sum of Divisors
53 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in FUNCTIONS
- Functions - confusion regarding properties, as per example in wiki
- Composition of functions - properties
- Finding Range from Domain
- Why is surjectivity defined using $\exists$ rather than $\exists !$
- What are the functions satisfying $f\left(2\sum_{i=0}^{\infty}\frac{a_i}{3^i}\right)=\sum_{i=0}^{\infty}\frac{a_i}{2^i}$
- Lower bound of bounded functions.
- Does there exist any relationship between non-constant $N$-Exhaustible function and differentiability?
- Given a function, prove that it's injective
- Surjective function proof
- How to find image of a function
Related Questions in UPPER-LOWER-BOUNDS
- Bound for difference between arithmetic and geometric mean
- Show that $\frac{1}{k}-\ln\left(\frac{k+1}{k}\right)$ is bounded by $\frac{1}{k^2}$
- Bounding Probability with Large Variance
- Connectivity of random graphs - proof $\frac{logn}{n}$ is threshold
- Natural log integral inequality
- Spectrum of a matrix after applying an element-wise function (e.g. elementwise log)
- Majorization form for a given set of integers in some interval.
- Proving $(λ^d + (1-λ^d)e^{(d-1)s})^{\frac{1}{1-d}}\leq\sum\limits_{n=0}^\infty\frac1{n!}λ^{\frac{(d^n-1)d}{d-1}+n}s^ne^{-λs}$
- Upper bound for distribution function of the standard normal distribution
- Show $0 < f'(x) \leqslant \frac{1}{2}$
Related Questions in DIVISOR-SUM
- Identify sequences from OEIS or the literature, or find examples of odd integers $n\geq 1$ satisfying these equations related to odd perfect numbers
- Characterize solutions of an equation involving the sum of divisors function and the Euler's totient function: Mersenne primes and Wagstaff primes
- Heuristics on the asymptotic behaviour of the divisor funcion
- What is the sum of reciprocal of product of $n$ primes?
- A reference request about the closed-form of $\sum_{n=1}^\infty\frac{\sigma(n^2)}{n^6}$, where $\sigma(n)$ denotes the sum of divisors functions
- What about the equation $\sigma(2n)=2\left(n+\sigma(n)\right),$ involving the sum of divisor function?
- Sum of non-trivial divisors of number equals number itself
- On the sum of divisors function.
- $\sigma(n) \equiv 1 \space \pmod{n}$ if and only if $n$ is prime
- Show that for $n\gt 2$, $\frac{\sigma_1(n)}{n}\lt H_n$
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?