Question 841526
I don't believe there is a fast way to determine whether an integer is abundant or not. Given *[tex \large n = p_1^{e_1}p_2^{e_2} \ldots p_k^{e_k}] we have


*[tex \large \sigma(n) = (1+p_1 + \ldots + p_1^{e_1})(1 + p_2 + \ldots + p_2^{e_2}) \ldots (1+p_k+\ldots + p_k^{e_k})]


and *[tex \large n] is abundant if *[tex \large \sigma(n) > 2n]. Note that if *[tex \large n] is abundant, then *[tex \large cn] is also abundant where *[tex \large c \in \mathbb{Z}^{+}].