The
L
2
{L^2}
theories are known of the summation formula involving
σ
k
(
n
)
{\sigma _k}(n)
, the sum of the kth power of divisors of n, as coefficients, for all k except
k
=
1
k = 1
. In this paper, techniques are used to overcome the extra convergence difficulty of the case
k
=
1
k = 1
, to establish a symmetric formula connecting the sums of the form
∑
σ
1
(
n
)
n
−
1
/
2
f
(
n
)
\sum {\sigma _1}(n){n^{ - 1/2}}f(n)
and
∑
σ
1
(
n
)
n
−
1
/
2
g
(
n
)
\sum {{\sigma _1}} (n){n^{ - 1/2}}g(n)
, where
f
(
x
)
f(x)
and
g
(
x
)
g(x)
are Hankel transforms of each other.