How this calculation works
For a prime p the sum is 1+p. To obtain the proper-divisor sum, subtract n from the reported total.
THE FORMULA
σ(n) = product of (1 + p + ⋯ + pᵉ)A worked example
28 has divisors 1, 2, 4, 7, 14 and 28, which sum to 56.
Good to know
The input must be positive.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Sum all positive divisors, including the input itself.
The primary result is labeled “Sum of divisors”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The input must be positive.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
28 has divisors 1, 2, 4, 7, 14 and 28, which sum to 56.
Which rule does this calculator apply?
σ(n) = product of (1 + p + ⋯ + pᵉ)