Problem Statement

An Abundant number is a number n for which the   sum of divisors   σ(n) > 2n, or,   equivalently,   the   sum of proper divisors   (or aliquot sum)       s(n) > n.

12   is abundant, it has the proper divisors     1,2,3,4 & 6     which sum to   16   ( > 12 or n);        or alternately,   has the sigma sum of   1,2,3,4,6 & 12   which sum to   28   ( > 24 or 2n).

Abundant numbers are common, though even abundant numbers seem to be much more common than odd abundant numbers. To make things more interesting, this task is specifically about finding   odd abundant numbers.

Let's start with the solution: