Formal Definition and Examples
Formally, a natural number n is called highly abundant if and only if for all natural numbers m < n,
where σ denotes the sum-of-divisors 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).
For instance, 5 is not highly abundant because σ(5) = 5+1 = 6 is smaller than σ(4) = 4 + 2 + 1 = 7, while 8 is highly abundant because σ(8) = 8 + 4 + 2 + 1 = 15 is larger than all previous values of σ.
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