Dedekind psi summatory function

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The Dedekind psi summatory function (partial sums of the Dedekind psi function) is

$\Psi (n):=\sum _{k=1}^{n}\psi (k)=\sum _{k=1}^{n}k\prod _{p|k}{\frac {p+1}{p}}$

where $\scriptstyle \psi (n)$ is the Dedekind psi function.

$\Psi (n)$ is even for $n>2.$

Sequences

A173290 Dedekind psi summatory function: partial sums of the Dedekind psi function (A001615).

{1, 4, 8, 14, 20, 32, 40, 52, 64, 82, 94, 118, 132, 156, 180, 204, 222, 258, 278, 314, 346, 382, 406, 454, 484, 526, 562, 610, 640, 712, 744, 792, 840, 894, 942, 1014, 1052, 1112, 1168, 1240, 1282, ...}