Convolution identities for twisted Eisenstein series and twisted divisor functions

Table 12 Table 12

	$σ_{1} (n) = n$	$σ_{1}^{*} (n) = n$		$σ_{1} (n) = n + 2$	$σ_{1}^{*} (n) = n + 2$
n	1	$2^{m}$ , $m \in N \cup {0}$	n	none	n = 2p, with p any odd prime
	$σ_{1} (n) = n + 1$	$σ_{1}^{*} (n) = n + 1$		$σ_{1} (n) = n + 3$	$σ_{1}^{*} (n) = n + 3$
n	prime	odd prime	n	4	none