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.
Read more about this topic: Highly Abundant Number
Famous quotes containing the words formal, definition and/or examples:
“Then the justice,
In fair round belly with good capon lined,
With eyes severe and beard of formal cut,
Full of wise saws and modern instances;
And so he plays his part.”
—William Shakespeare (1564–1616)
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)