I was looking into this sequence. And I'm particularly interested in the asymptotic behavior of the following series (which is stated on the site) $$\sum_{k=1}^n \frac{1}{a(k)} \sim \frac{3\log(n)^2}{(2\pi^2)} + \cdots, $$ where $a(k) = \min\{k \in \mathbb{N}: n \mid k^2 \}$. But I couldn't find any further details about it on the site, except for the author Vaclav Kotesovec, but with no success finding any further details about the series. Can you provide me with some relevant references, please? ${}$

I was looking into this sequence. And I'm particularly interested in the asymptotic behavior of the following series (which is stated on the site) $$\sum_{k=1}^n \frac{1}{a(k)} \sim \frac{3(\log n)^2}{2\pi^2} + \cdots, $$ where $a(k) = \min\{m \in \mathbb{N}: k \mid m^2 \}$. But I couldn't find any further details about it on the site, except for the author Vaclav Kotesovec, but with no success finding any further details about the series. Can you provide me with some relevant references, please?

I was looking into this sequence. And I'm particularly interested in the asymptotic behavior of the following series (which is stated on the site) $$\sum_{k=1}^n \frac{1}{a(k)} \sim \frac{3\log(n)^2}{(2\pi^2)} + \cdots, $$ where $a(k) = \min\{k \in \mathbb{N}: n \mid k^2 \}$. But I couldn't find any further details about it on the site, except for the author Vaclav Kotesovec, but with no success finding any further details about the series. Can you provide me with some relevant references, please?

I was looking into this sequence. And I'm particularly interested in the asymptotic behavior of the following series (which is stated on the site) $$\sum_{k=1}^n \frac{1}{a(k)} \sim \frac{3\log(n)^2}{(2\pi^2)} + \cdots, $$ where $a(k) = \min\{k \in \mathbb{N}: n \mid k^2 \}$. But I couldn't find any further details about it on the site, except for the author Vaclav Kotesovec, but with no success finding any further details about the series. Can you provide me with some relevant references, please? ${}$