If we act a little more shrewdly, however, we can discover this counter-example more quickly than if we unthinkingly test one odd number after another. For a number to have a large aliquot sum, it needs lots of factors and large factors at that, which themselves come from being paired with small factors. We can therefore build numbers with large aliquot sums by multiplying small primes together. If we are focusing on odd numbers only, we should look at those that are products of the first few odd primes,which are 3, 5, 7, etc. This rule of thumb would soon lead you to test 33×5×7=945 and thereby discover the abundance property among the odd numbers also.