Sir
In her informative Book Review of Yoko Ogawa's The Housekeeper and the Professor (Nature 460, 461–462; 2009), Jennifer Rohn nicely illustrates how one false premise will lead to all kinds of misunderstanding. She states that primes resist “division by any number other than zero and one”. She means, of course, that a prime number resists division by any number other than itself and one. Every integer can count on two divisors: itself and one. All resist division by zero.
If we do not exclude unity and the number itself when summing up divisors, the 'abundant' numbers, whose divisors' sum is greater than themselves (for example, the number 18 referred to in the review), really would be abundant — and would include all numbers higher than one. Meanwhile, 'deficient' numbers such as the number 14, for which the divisors' sum is less, would be non-existent.
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Speijer, D. Defining numbers in terms of their divisors. Nature 461, 37 (2009). https://doi.org/10.1038/461037c
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DOI: https://doi.org/10.1038/461037c
