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Associated to the least common multiple ${\\rm lcm}_{0\\le i\\le k}\\{f(n+i)\\}$ of any $k+1$ consecutive terms in the quadratic progression $\\{f(n)\\}_{n\\in \\mathbb{N}^*}$, we define the function $g_{k, f}(n):=(\\prod_{i=0}^{k}|f(n+i)|)/{\\rm lcm}_{0\\le i\\le k}\\{f(n+i)\\}$ for all integers $n\\in \\mathbb{N}^*\\setminus Z_{k, f}$, where $Z_{k,f}:=\\bigcup_{i=0}^k\\{n\\in \\mathbb{N}^*: f(n+i)=0\\}$. 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Associated to the least common multiple ${\\rm lcm}_{0\\le i\\le k}\\{f(n+i)\\}$ of any $k+1$ consecutive terms in the quadratic progression $\\{f(n)\\}_{n\\in \\mathbb{N}^*}$, we define the function $g_{k, f}(n):=(\\prod_{i=0}^{k}|f(n+i)|)/{\\rm lcm}_{0\\le i\\le k}\\{f(n+i)\\}$ for all integers $n\\in \\mathbb{N}^*\\setminus Z_{k, f}$, where $Z_{k,f}:=\\bigcup_{i=0}^k\\{n\\in \\mathbb{N}^*: f(n+i)=0\\}$. 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