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We show that $n$ is almost perfect if and only if $I(n) - 1 < D(n) \leqI(n)$, where $I(n)$ is the abundancy index of $n$ and $D(n)$ is the deficiencyof $n$. This criterion is then extended to the case of integers $m$ satisfying$D(m)>1$.

A Criterion for Deficient Numbers Using the Abundancy Index and Deficiency Functions