Table 2 Convolution formulas for prime $\mathit{p}\mathbf{=}\mathbf{2}\mathit{q}\mathbf{+}\mathbf{1}$

${\sum }_{k=1}^{p-1}{\sigma }_1(k){\sigma }_1(p-k)$

$\frac{1}{3}q(10q^2+9q-1)$

${\sum }_{k=1}^{p-1}{\sigma }_1^{\ast }(k){\sigma }_1^{\ast }(p-k)$

$2q^2(q+1)$

${\sum }_{k=1}^{p-1}{\sigma }_1(k){\sigma }_3(p-k)$

$\frac{1}{15}q(42q^4+75q^3+50q^2+15q-2)$

${\sum }_{k=1}^{p-1}{\sigma }_1^{\ast }(k){\sigma }_3^{\ast }(p-k)$

$q^2(q+1)(2q^2+2q+1)$

${\sum }_{r+s+t=p}{\sigma }_1(r){\sigma }_1(s){\sigma }_1(t)$

$\frac{1}{12}{q}^2(14q^3+5q^2-8q+1)$

${\sum }_{r+s+t=p}{\sigma }_1^{\ast }(r){\sigma }_1^{\ast }(s){\sigma }_1^{\ast }(t)$

$\frac{1}{2}{q}^4(q+1)$