Highly abundant number
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In mathematics, a highly abundant number is a certain kind of natural number. Formally, a natural number n is called highly abundant if and only if for all m < n,
- σ(n) > σ(m)
where σ denotes the divisor function. The first few highly abundant numbers are 1, 2, 3, 4, 6, 8, 10, 12, 16, 18, 20, 24, 30, 36, 42, 48, 60, ... (sequence A002093 in OEIS).
All integer values of the factorial are highly abundant numbers, as are all colossally abundant numbers.
[edit] See also
- Colossally abundant number
- Superabundant number
- Abundant number
- Deficient number
- Highly composite number
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