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Weird Numbers

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

Weird Numbers

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Presentation Transcript

1. Weird Numbers Jason Holman • Mathematics • Number Theory • Computational Number Theory

2. Types of number to be discussed • Abudnant • Deficient • Perfect • Pseudoperfect

3. 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

4. Deficient • An integer is deficient if the sum of its proper divisors is less than the number • Examples • 35, 50, primes

5. Perfect • An integer is perfect if the sum of its proper divisors is equal to the number • Examples • 6, 28

6. Pseudoperfect • An integer is pseudoperfect if a subset of its proper divisors is equal to the number • Examples • 18, 24

7. Definition of weird number • A number is weird if it is abundant but not pseudoperfect

8. Examples of weird numbers • The first few weird numbers are 70, 836, 4030, 5830, 7192, 9272 • Example of how 70 is weird

9. 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

10. Sources • http://blogs.ams.org/mathgradblog/2013/08/29/odd-weird-numbers/ • http://mathworld.wolfram.com/WeirdNumber.html

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