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Natural density of integers such that $\forall 1\leq k\leq n-1$ satisfy $\operatorname{rad}(k)+\operatorname{rad}(n-k)\geq \operatorname{rad}(n)$
For an integer $n>1$ we defined its square-free kernel $$\operatorname{rad}(n)=\prod_{\substack{p\mid n\\p \text{ prime}}}p$$
as the product of distinct prime factors dividing it, with the ...
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