Weird Numbers

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## Weird Numbers

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**Weird Numbers**Jason Holman • Mathematics • Number Theory • Computational Number Theory**Types of number to be discussed**• Abudnant • Deficient • Perfect • Pseudoperfect**Abundant**• An integer is abundant if the sum of its proper divisors (all except the number itself) is greater than the number • Examples • 18, 24**Deficient**• An integer is deficient if the sum of its proper divisors is less than the number • Examples • 35, 50, primes**Perfect**• An integer is perfect if the sum of its proper divisors is equal to the number • Examples • 6, 28**Pseudoperfect**• An integer is pseudoperfect if a subset of its proper divisors is equal to the number • Examples • 18, 24**Definition of weird number**• A number is weird if it is abundant but not pseudoperfect**Examples of weird numbers**• The first few weird numbers are 70, 836, 4030, 5830, 7192, 9272 • Example of how 70 is weird**Big picture problem**• No known odd weird numbers • The weird numbers known so far have been computed either manually or using a computer • It is believed that an equation would help find the answer to this problem, but one has not been found • So the answer to this problem currently relies on extremely tedious computations**Sources**• http://blogs.ams.org/mathgradblog/2013/08/29/odd-weird-numbers/ • http://mathworld.wolfram.com/WeirdNumber.html