Table 4 ${\mathbf{\sum }}_{\mathit{k}\mathbf{=}\mathbf{1}}^{\mathit{N}\mathbf{-}\mathbf{1}}{\mathit{\sigma }}_{\mathbf{1}}^{\mathbf{\ast }}\mathbf{(}{\mathbf{2}}^{\mathit{m}}\mathit{k}\mathbf{;}\mathbf{2}\mathbf{)}{\mathit{\sigma }}_{\mathbf{1}}^{\mathbf{\ast }}\mathbf{(}{\mathbf{3}}^{\mathit{n}}\mathbf{(}\mathit{N}\mathbf{-}\mathit{k}\mathbf{)}\mathbf{;}\mathbf{3}\mathbf{)}$ and ${\mathbf{\sum }}_{\mathit{k}\mathbf{=}\mathbf{1}}^{\mathit{N}\mathbf{-}\mathbf{1}}{\mathit{\sigma }}_{\mathbf{1}}\mathbf{(}{\mathbf{2}}^{\mathit{m}}\mathit{k}\mathbf{)}{\mathit{\sigma }}_{\mathbf{1}}\mathbf{(}{\mathbf{3}}^{\mathit{n}}\mathbf{(}\mathit{N}\mathbf{-}\mathit{k}\mathbf{)}\mathbf{)}$

${\sum }_{k=1}^{N-1}{\sigma }_1^{\ast }(2^{m}k;2){\sigma }_1^{\ast }(3^n(N-k);3)$

$\begin{array}{l}\frac{2^m\cdot 3^n}{120}[36\{{\sigma }_3^{\ast }(N)-{\sigma }_3^{\ast }(\frac{N}{3})\}-20N{\sigma }_1^{\ast }(N)\\ -15N{\sigma }_1^{\ast }(N;3)-a(N)]\end{array}$

${\sum }_{k=1}^{N-1}{\sigma }_1(2^{m}k){\sigma }_1(3^n(N-k))$

$\begin{array}{l}\frac{1}{240}[(2^{m+3}-3)(3^{n+3}-7){\sigma }_3(N)\\ -8(2^m-1)(3^{n+3}-7){\sigma }_3(\frac{N}{2})\\ -27(2^{m+3}-3)(3^n-1){\sigma }_3(\frac{N}{3})\\ +216(2^m-1)(3^n-1){\sigma }_3(\frac{N}{6})\\ -5\{3-2^{m+2}-3^{n+1}\\ +6(7\cdot 2^m\cdot 3^n-2\cdot 3^n-2^m)N\}{\sigma }_1(N)\\ +20(2^m-1)(2\cdot 3^{n+1}N-1){\sigma }_1(\frac{N}{2})\\ +15(3^n-1)(3\cdot 2^{m+1}N-1){\sigma }_1(\frac{N}{3})\\ -6(2^m-1)(3^n-1)a(N)]\end{array}$