An asymptotic formula related to the sums of divisors
Volume 175 / 2016
Acta Arithmetica 175 (2016), 183-200
MSC: 11N37, 11P55, 11L03.
DOI: 10.4064/aa8391-5-2016
Published online: 19 September 2016
Abstract
Let $d(n)$ be the number of divisors of $n$, and $k$ a positive integer. It is proved that the sum $\sum_{1\leq m_1,\dots,m_s\leq X}d(m_1^k+\cdots+m_s^k)$ has an asymptotic formula for $k\geq2$ and $s \gt \min\{2^{k-1}, k^2+k-2\}.$
