Difference between revisions of "Abundant number"
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An '''abundant number''' is a number <math>n</math> for which the sum of its [[proper divisor|proper divisors]] is greater than <math>n</math> itself. For example, 12 is abundant because the sum of its proper divisors is 1 + 2 + 3 + 4 + 6 = 16 > 12. | An '''abundant number''' is a number <math>n</math> for which the sum of its [[proper divisor|proper divisors]] is greater than <math>n</math> itself. For example, 12 is abundant because the sum of its proper divisors is 1 + 2 + 3 + 4 + 6 = 16 > 12. | ||
| − | =Examples= | + | ==Examples== |
The first 10 abundant numbers are: | The first 10 abundant numbers are: | ||
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945, 1575, 2205, 2835, 3465, 4095, 4725, 5355, 5775, 5985,... | 945, 1575, 2205, 2835, 3465, 4095, 4725, 5355, 5775, 5985,... | ||
| + | ==Properties== | ||
| + | There are infinitely many abundant numbers. | ||
| + | Every positive multiple of an abundant number is an abundant number. | ||
| + | Every multiple of a perfect number greater than itself is an abundant number. | ||
| + | ==See also== | ||
| + | [[Perfect Number]] | ||
| + | [[Deficient Number]] | ||
{{stub}} | {{stub}} | ||
Revision as of 21:00, 6 February 2018
An abundant number is a number 
for which the sum of its proper divisors is greater than itself. For example, 12 is abundant because the sum of its proper divisors is 1 + 2 + 3 + 4 + 6 = 16 > 12.
Examples
The first 10 abundant numbers are:
12, 18, 20, 24, 30, 36, 40, 42, 48, 54,...
The first 10 odd abundant numbers are:
945, 1575, 2205, 2835, 3465, 4095, 4725, 5355, 5775, 5985,...
Properties
There are infinitely many abundant numbers. Every positive multiple of an abundant number is an abundant number. Every multiple of a perfect number greater than itself is an abundant number.
See also
Deficient Number This article is a stub. Help us out by expanding it.
