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Abundant number information


Demonstration, with Cuisenaire rods, of the abundance of the number 12

In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The integer 12 is the first abundant number. Its proper divisors are 1, 2, 3, 4 and 6 for a total of 16. The amount by which the sum exceeds the number is the abundance. The number 12 has an abundance of 4, for example.

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Abundant number

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In number theory, an abundant number or excessive number is a positive integer for which the sum of its proper divisors is greater than the number. The...

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Colossally abundant number

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In number theory, a colossally abundant number (sometimes abbreviated as CA) is a natural number that, in a particular, rigorous sense, has many divisors...

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Highly abundant number

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In number theory, a highly abundant number is a natural number with the property that the sum of its divisors (including itself) is greater than the sum...

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Primitive abundant number

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primitive abundant number is an abundant number whose proper divisors are all deficient numbers. For example, 20 is a primitive abundant number because:...

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2

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whereas an abundant number has a sum of its proper divisors that is larger than the number itself. Primitive abundant numbers are abundant numbers whose...

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Weird number

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In number theory, a weird number is a natural number that is abundant but not semiperfect. In other words, the sum of the proper divisors (divisors including...

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