On the $2$-adic valuation of ${\sigma }_k(n)$

Kaimin Cheng, Ke Zhang

For a positive integer $k$, let \[ σ_k(n)=\sum_{d\mid n} d^k \] be the divisor function of order $k$, and let ${\nu }_p(m)$ denote the $p$-adic valuation of an integer $m$. Motivated by…