How this calculation works
A perfect number equals the sum of its proper divisors. For example, 6 = 1+2+3.
THE FORMULA
Compare the sum of proper divisors with nA worked example
The proper divisors of 12 sum to 16, so it is abundant.
Good to know
For 1 the proper-divisor sum is zero.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Classify a number by adding its positive divisors below the number itself.
The primary result is labeled “Classification”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
For 1 the proper-divisor sum is zero.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
The proper divisors of 12 sum to 16, so it is abundant.
Which rule does this calculator apply?
Compare the sum of proper divisors with n