Despite these discoveries, you might still think it likely that, just as there seem to be no odd perfect numbers, there are no odd abundant numbers either. In other words, our modified conjecture might be that all odd numbers are deficient. Calculation of the aliquot sums of the first few hundred odd numbers would seem to confirm this theory, but the claim is eventually debunked upon testing 945, which has 97s as the sum of its proper divisors. Now the floodgates open as any multiple of an abundant number is abundant, and in particular the odd multiples of 945 immediately supply us with infinitely many more odd abundant numbers.
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