Weird numbers

Weird numbers

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Caption: The first 17 weird numbers. A weird number is an abundant number that is not semi-perfect. Abundant numbers are ones where the sum of proper divisors total that or a greater number. A semi-perfect number is one whose divisors, or a subset of, total that number exactly. For example the divisors of 12 (the smallest abundant number) are 1, 2, 3, 4 and 6, and total 16. The subset 2, 4, 6 total 12. Hence it is also semi-perfect. Only a tiny proportion of abundant numbers are not semi-perfect. Illustration.

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