NUMBER LAB · EXPLORE WITH CONFIDENCE

Abundant, Perfect & Deficient Number Explorer

Classify an interval by proper-divisor sums and filter abundant, perfect or deficient numbers with an auditable numeric report.

Worked examplesBrowser processingTXT · CSV · JSON

Explore the example, or adjust the inputs. Save a project to keep your settings.

A useful starting point

6 is perfect because 1 + 2 + 3 = 6. 12 is abundant because its proper divisors sum to 16; 8 is deficient because they sum to 7.

Scope and limits

Endpoints 1–200,000 and a span no larger than 5,000. Counts cover the interval; the table and exports follow the selected classification.

Calculations run in your browser. Projects are saved only when you download them. Website advertising and analytics follow the privacy and consent settings. Import large integer CSV columns as text in spreadsheets to preserve their digits.

Using Abundant, Perfect & Deficient Number Explorer

Classify an interval by proper-divisor sums and filter abundant, perfect or deficient numbers with an auditable numeric report.

Choose a worked example or enter your own values in the labeled controls.
Adjust the available options. Results refresh when you leave a field or choose an option.
Review the result summary, interpretation and calculation table. Check any explicit limits or assumptions.
Copy the text or download TXT, CSV or JSON. Save a project to reopen the same inputs later.

Example

6 is perfect because 1 + 2 + 3 = 6. 12 is abundant because its proper divisors sum to 16; 8 is deficient because they sum to 7.

Questions & answers

Does the divisor sum include the number itself?

No. Proper positive divisors exclude the number being classified.

Why are the summary counts unchanged when I filter?

The summary describes the entire interval. The matching-row count and exported records reflect your chosen filter.

Can I save and reopen my settings?

Yes. Save project downloads a JSON file for this tool. Open project restores it; undo and redo work during the current session.

Does the table contain every result?

The table is paginated in groups of 50. Downloads contain all listed rows. The partition tool intentionally caps its example listing while reporting the full exact count.