I would like to ask about the next question that seems to me interesting. I know an article that was written by Andrzej Schinzel in which he stated Lemma 2. In this post we denote the Dedekind psi function is defined for a positive integer $m>1$ as the arithmetic function
$$\psi(m)=m\prod_{\substack{p\mid m\\p\text{ prime}}}\left(1+\frac{1}{p}\right),\tag{1}$$ with the definition $\psi(1)=1$. See the Wikipedia Dedekind psi function. As refers Wikipedia it is the sequence A001615 in the OEIS. I've edited several problems related to (problems involving) this interesting arithmetic function, but I don't know much about it, this is the motivation of this question (the claims from Wikipedia or the comments in OEIS).
Question. Consider $$\psi(y_1)+\ldots+\psi(y_t)\leq B(k)\tag{2}$$ over positive integers $y_i$ with $1\leq i\leq t$ and $B(k)=\operatorname{bound}(k)$ a suitable bound that is a function of the variable $k\geq 1$, $k\in\mathbb{Z}$. Determine such suitable $B(k)$ with the purpose to get an upper bound $\mathcal{B}(k)$ of $$\operatorname{lcm}[y_1,\ldots,y_t],$$ that's to get a statement $$\operatorname{lcm}[y_1,\ldots,y_t]\leq \mathcal{B}(k).\tag{3}$$ Many thanks.
The function $\operatorname{lcm}[y_1,\dots,y_t]$ means the least common multiple. I'm inspired in the mentioned lemma from [1], and I'm asking what work can be done about it to get a statament at research level.
References:
[1] A. Schinzel, Around Pólya's Theorem on Prime Divisors of a Linear Recurrence, Diophantine Equations, pages 225-233, TIFR edited by N. Saradha, Narosa Publishing House (2008).
