Evaluation of certain convolution sums involving the sum of the divisors function

We evaluate the convolution sums ∑rl+sm=nσ(l)σ(m)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\sum _{rl+sm=n}\sigma (l)\sigma (m)$$\end{document}, for (r,s)=(1,17),(1,34),(2,17),\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ (r,s)=(1,17),(1,34),(2,17),$$\end{document} (1, 68) and (4, 17), for all positive integers n.\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n\mathbf {.}$$\end{document} We then use these evaluations to determine formula for the number of representation of a positive integer n by the octonary quadratic form x12+x22+x32+x42+17(x52+x62+x72+x82).\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ x_{1}^{2}+x_{2}^{2}+x_{3}^{2}+x_{4}^{2}+17\big (x_{5}^{2}+x_{6}^{2}+x_{7}^{2}+x_{8}^{2}\big ).$$\end{document}