NUMBER LAB · SEE THE PATTERN

Abundant, Perfect & Deficient Number Explorer

See which numbers in a range are abundant, perfect or deficient, and pick any number to see exactly why.

Number mapWorked proofTXT · CSV · JSON

MinimumMaximum

Number	Proper divisor sum	Difference	Kind

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Scope and limits

Range endpoints 1–200,000 and a span no larger than 5,000. Counts cover the whole range; the table and exports follow the selected kind. Click a kind again to show all. One is deficient because its proper-divisor sum is zero.

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 starting range, or enter your own minimum and maximum.
Click Abundant, Perfect or Deficient to highlight that kind on the map and filter the table.
Click any number, or type one, to see its proper divisors, their sum and why it gets that name.
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.