Asian Journal of Mathematics and Computer Research

THE CONVOLUTION SUMS ∑m<n/4 m2σe(m) σf(n-4m)

AERAN KIM *

A Private Mathematics Academy, 1599-6-bungi, Keumam-2-dong, Deokjin-gu, Jeonju-si, Jeollabuk-do, 561-806, South Korea.

*Author to whom correspondence should be addressed.

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Abstract

As following the same method in [1], [2], [3], and [4], we obtain some convolution sum formulae related to

∑m<n/4 m2σe(m) σf(n-4m)

for an odd positive integer e and f where 1 ≤ e, f ≤ 5 Moreover we deduce a few of identities from the above convolution sum.

Keywords: Divisor functions, convolution sums

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