Asian Journal of Mathematics and Computer Research

THE CONVOLUTION SUMS ∑m<n/3 σ3 (m) σ7 (n-3m), ∑m<n/3 σ7 (m) σ3 (n-3m), ∑m<n/3 σ5 (m) σ5 (n-3m), AND THE COEFFICIENTS RELATIONS

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

In this article we obtain some convolution sum formulae as

∑m<n/3 σ3 (m) σ7 (n-3m), ∑m<n/3 σ7 (m) σ3 (n-3m)

and 

∑m<n/3 σ5 (m) σ5 (n-3m)

for all n ∈ N.

Keywords: Divisor functions, Infinite product sums;, Convolution sums

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