MATH
Login Or Sign up

List Question

15
2.3k
Views

Is $\ 7!=5040\ $ the largest highly composite factorial?

Published on
#number-theory #factorial #divisor-counting-function
96
Views

Let $s_k$ be the $lcm$ of the numbers $1$ to $k$. Is $s_{28}$ the largest highly composite such number?

Published on
#number-theory #prime-factorization #least-common-multiple #divisor-counting-function
168
Views

How reliable is the list of HCN-numbers considering this link?

Published on
#number-theory #prime-factorization #divisor-counting-function
1k
Views

Prime dividing sum of divisors

Published on
#prime-numbers #divisibility #factoring #divisor-counting-function
143
Views

On $-\log (2\pi)\sigma_0(n)-\frac{1}{2}\sum_{1<d\mid n}\log\left(\frac{1+2d}{(d+1)^2}\right),$ where $\sigma_0(n)=\sum_{d\mid n}1$ and its twists

Published on
#asymptotics #analytic-number-theory #divisor-sum #divisor-counting-function
46
Views

Counting functions and subsets

Published on
#binomial-coefficients #binomial-theorem #divisor-counting-function
83
Views

On the sequence of positive integers satisfying $\sigma(n)\mid (n(\sigma_0(n))^2)$

Published on
#sequences-and-series #elementary-number-theory #reference-request #divisor-sum #divisor-counting-function
76
Views

The function $f(n) ={\ln(\tau(n)) \above 1.5pt \ln(2)}$ and the number $2^{\tau(n)}+1$

Published on
#real-analysis #prime-numbers #logarithms #divisor-counting-function
188
Views

Prove that $\nu(n) \le \nu(2^{n}-1)$ where $\nu(n)$ is the number of positive divisors of n

Published on
#elementary-number-theory #inequality #divisor-counting-function
1.5k
Views

Formula for square of the number of divisors $\sum_{r\mid n} d(r^2) = d^2(n)$

Published on
#summation #analytic-number-theory #arithmetic-functions #multiplicative-function #divisor-counting-function
157
Views

Computing the bound of $d(n)$ the divisor counting "function" of $n$

Published on
#algebra-precalculus #elementary-number-theory #inequality #asymptotics #divisor-counting-function
65
Views

Which of these two expressions (related to primes) is greater: $\frac{\sigma{(n)}}{n}$ or $\sum_{p \le n}{\frac{1}{p}}$?

Published on
#elementary-number-theory #inequality #prime-numbers #divisor-sum #divisor-counting-function
196
Views

Prove that: $xy = 96$ has $24$ possible integer solutions.

Published on
#combinatorics #elementary-number-theory #divisor-counting-function
327
Views

show that $ \sum_{n \leq z} \frac{\tau(n)}{n} = \frac{1}{2} \log^2 z + c_2 \log z + c_3 + O(\sqrt[4]{z})$

Published on
#prime-numbers #analytic-number-theory #divisor-counting-function
178
Views

If $a(n)=n^2+1$ then $\gcd(a_n,2^{d(a_n)})=1\text{ or }2$?

Published on
#algebra-precalculus #elementary-number-theory #gcd-and-lcm #divisor-counting-function

Trending Questions

Popular # Hahtags

geometry circles algebraic-number-theory functions real-analysis elementary-set-theory proof-verification proof-writing number-theory elementary-number-theory puzzle game-theory calculus multivariable-calculus partial-derivative complex-analysis logic set-theory second-order-logic homotopy-theory winding-number ordinary-differential-equations numerical-methods derivatives integration definite-integrals probability limits sequences-and-series algebra-precalculus

Popular Questions

Copyright © 2021 JogjaFile Inc.