The Wendt binomial circulant determinant $W_n$ can be defined quite simply as a resultant: $$ W_n = \operatorname{res}(x^n-1, (x+1)^n-1). $$ Truer to its name, one may also define it as the determinant $\det(A)$ of the circulant matrix with entries $A_{i,j} = \binom{n}{\lvert i-j\rvert}$. The We...

After a few computations in wolfram alpha about the divisor function for some values of $n$ to look the behavior of $\sigma_x(n)\bmod n$ for $\,n=6,\,$ i got this result : $\sigma_x(6)=0 \bmod 6$ for $x$ odd and 2 mod 6 if $x$ is even Edit:01 :${\sigma}_x(n) =\sum_{d|n} d^x$ is the sum divisor ...

Edit 01:In order to look divisibility among power divisor function where i would like to know if there a such integer $n>1 $ with y coprime to $x$ then we have: :$\sigma_y(n)\bmod \sigma_x(n)=0$, by wolfram alpha i have got no integer n>1 satisfies the equation $\sigma_y(n)\bmod \sigma_x(n)=0$ ...

Really i'm interesting to check solutions of equations which it is related to sum divisor function .I accrossed the below equation which i got only one integer solution using wolfram alpha as shown here. My question here: Is $n=5$ the only integer satisfy the equation :$\sigma((n-1)!+1))=\sig...

This question is related to my question here , I w'd like to check if $n \geq 1:\sigma(n!-1) $ never be prime according to some computations which i did in wolfram alpha to come up with parity of sum power divisor function at $n!-1$ for some integer $n$ i observed that $\sigma(n!-1)\bmod 10 $ at ...

I am looking for pairs of positive integers $(m,n)$ such that $ \sigma(n!-1) =m^2$, where $\sigma$ is the sum of divisors function. Examples occur with $(m,n)=(12,5),(1,2)$. Question: Are there others?

It is a result of Carmichael that for any integer $n > 12$, the Fibonacci number $F_n$ has at least one primitive divisor, that is, a prime factor $p$ such that $p$ does not divide any $F_m$ with $1 \leq m < n$. Indeed, a more general result for all Lucas and Lehmer sequences has been proven by B...