Divisor Sum Calculator
Sum the positive divisors of a positive integer via its prime factorization.
Description
Sum the positive divisors of a positive integer via its prime factorization.
Sum the positive divisors of a positive integer via its prime factorization.
When to use Divisor Sum Calculator
Use this tool to test or transform exact integers according to the named number-theory definition, for education, validation, or algorithm checks.
- Integer
- An integer input greater than or equal to 1.
How the calculation works
The formula below determines the tool output. Divisor sum: The calculated divisor sum.1
if n = Πpᵢ^aᵢ, then σ(n) = Π((pᵢ^(aᵢ+1) − 1) / (pᵢ − 1)) Limitations and assumptions
This tool applies an exact integer definition within JavaScript's safe-integer range. It is not an arbitrary-precision factorization or proof system, so do not use rounded measurements or integers beyond the accepted domain as though they were exact.
Alternative or Complementary approaches
Complement a number-property result with its factorization, divisors, digit representation, or a second independent predicate. A true result establishes only the named property and does not imply other properties such as primality.
References
-
Divisor function — Wikipedia contributors
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Count the positive divisors of a positive integer via its prime factorization.