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An abundant number (also known as excessive numbers) is a positive integer such that the sum of its proper divisors is greater than the number itself. Or equivalently, a positive integer \(n\) is said to be abundant if \(\sigma_1 (n) > 2n\), where \(\sigma_1(n) \) denotes the sum of factors of \(n\).
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.
8 Αυγ 2023 · In number theory, “an abundant number is a positive integer that is smaller than the sum of its proper divisors. The proper divisors of a number are all its positive divisors excluding itself”. In other words, “an abundant number n is one for which the sum of its proper divisors is greater than n ”. Examples:
Abundant numbers are positive integers for which the sum of their proper divisors exceeds the number itself. This means that when you add up all the factors of a number, excluding the number, the total is greater than the number.
I am a high school math teacher and I am looking for a comprehensive list of large numbers which occur in real world. For example. There are $10^{14}$ cells in the human body; $10^{100}$ is called googol and the name google is derived from this... There are $6\cdot 10^{23}$ atoms/molecules in one mole
An abundant number or excessive number is a number for which the sum of its proper divisors is greater than the number itself. An abundant number is a number n for which the sum of divisors σ(n)>2n, or, equivalently, the sum of proper divisors (or aliquot sum) s(n)>n. Example: 48 is a abundant number. 1 and 48. 2 and 24. 3 and 16. 4 and 12. 6 ...
Abundant numbers are positive integers for which the sum of their proper divisors (excluding the number itself) is greater than the number.
