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We say that a proper ideal $I$ of $R$ is $\\phi$-$n$-absorbing primary if whenever $a_1,a_2,...,a_{n+1}\\in R$ and $a_1a_2\\cdots a_{n+1}\\in I\\backslash\\phi(I)$, either $a_1a_2\\cdots a_n\\in I$ or the product of $a_{n+1}$ with $(n-1)$ of $a_1,...,a_n$ is in $\\sqrt{I}$. 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