This tool generates a list of excessive numbers, also known as abundant numbers. These are integers whose proper divisors (excluding the number itself) add up to more than the number itself. For example, 12 is excessive because its divisors (1, 2, 3, 4, 6) sum to 16.
You can control how the sequence is displayed, toggle index numbers, and export or copy the output instantly. The result updates live and flashes every time it changes.
How to Use:
- Enter how many excessive numbers you want in the input field.
- Choose how you want them displayed:
- Toggle line-by-line or inline output.
- Turn index numbers on or off.
- Watch the output update live in the right-hand box.
- Click “Copy Output” to copy the results.
- Click “Export to File” to download the sequence.
- Use “Clear All” to reset everything.
What Generate Excessive Number Sequence can do:
The tool finds numbers where the sum of all proper divisors is greater than the number itself. These start with 12, 18, 20, and continue with many others that appear throughout number theory.
You can format the output however you like one per line or in a single line and optionally label each result with its index. A live counter keeps track of how many have been generated, and output flashes on every change so you know it’s fresh.
Example:
Input:
10Settings: Line-by-line: ON, Show index: OFF
Output:
12
18
20
24
30
36
40
42
48
54Common Use Cases:
Great for exploring divisor functions, teaching number properties, or building data sets where abundance matters. Excessive numbers are useful in mathematics, cryptography, and systems modeling, and this tool gives you a fast, flexible way to explore them in bulk.
Useful Tools & Suggestions:
Looking at excessive numbers? You might want to compare them with Generate Deficient Number Sequence to see how they differ in divisor sums. And if you’re curious about perfect balance, Generate Perfect Numbers gives you examples where everything adds up just right.