Generate Almost Perfect Numbers
Quickly create a list of slightly defective numbers. Runs entirely in your browser, so your data never leaves your device.
Output
The result appears here as you type.
How to use Generate Almost Perfect Numbers
- 1. Set how many terms to generate. Enter How many terms to control the length of the sequence. Ten terms already reveals the pattern, since almost perfect numbers are simply powers of two.
- 2. Choose a separator. Set Separator to a comma, space or newline depending on where you are pasting the sequence, matching plain text, CSV or a one-per-line list.
- 3. Read the generated sequence. The tool lists numbers whose proper divisors sum to exactly one less than the number itself, starting from 1, 2, 4, 8, 16, and continuing through powers of two.
- 4. Copy the sequence. Copy the list into a number theory worksheet, a script's test data, or notes exploring the connection between almost perfect numbers and powers of two.
When to use Generate Almost Perfect Numbers
Generate Almost Perfect Numbers lists numbers whose proper divisors sum to exactly one less than the number itself, also called least deficient numbers. Every known example is a power of two, and whether any non-power-of-two example exists is an open question in number theory.
- Teaching the powers-of-two pattern in number theory. Every power of two is almost perfect, since its divisors 1, 2, 4 and so on up to half the number sum to one less than the number, a clean example to verify by hand.
- Introducing an open problem in number theory. Whether a non-power-of-two almost perfect number exists is unsolved, making this sequence a good entry point for discussing open problems alongside settled results like perfect numbers.
- Verifying a divisor sum function against known cases. A unit test for divisor sum code can check that it correctly identifies 8 or 16 as almost perfect, using the generated sequence as a known-correct reference.
- Comparing deficient, perfect and almost perfect numbers. A lecture covering the full classification of numbers by divisor sum benefits from a ready list of almost perfect examples to place alongside abundant and perfect number sequences.
Examples
The first ten almost perfect numbers
Output
1, 2, 4, 8, 16, 32, 64, 128, 256, 512
About the Generate Almost Perfect Numbers tool
Generate Almost Perfect Numbers is a free online tool that works entirely inside your web browser. Quickly create a list of slightly defective numbers. Because the processing happens on your own device, nothing you enter is uploaded, logged or stored anywhere.
This page is one of 234 Math utilities on EditSafely. Each one does a single job well, and all of them follow the same rule: your input stays on your machine.
You can shape the output with 2 settings, including How many terms and Separator, and the result refreshes the moment you change one. A worked example further down the page shows exactly what the tool produces for a real input.
Because nothing leaves your device, the tool is suitable for sensitive content such as internal documents, credentials or customer data. It also responds instantly, since every keystroke is handled on your own machine rather than by a remote API.
Frequently asked questions
Does Generate Almost Perfect Numbers cost anything?
Yes, it is completely free. All 2,658 tools on EditSafely work without an account, a subscription or usage limits.
Does the generator send anything to a server?
No data leaves your device. The whole tool is JavaScript that runs inside your browser tab, so there is no upload, no server-side processing and no log of what you did. If you disconnect from the internet after the page loads, it keeps working.
How do I get a different result?
Run the generator again. Each run is computed fresh on your device, and any options you change are applied to the next result immediately.
Do I need to sign up or install anything?
Nothing to install and no account needed. Open the page in any up-to-date browser, including on a phone or tablet, and the tool is ready.
How do I use the result?
The output panel has a one-click copy button, and you can keep refining the input while you work; the result updates in place as you type.