Deficiency Ratio Calculator
Signed deficiency ratio[n−s(n)]/n, proper divisors sum, npositive≤1e6, negative for abundant; not σ(n)/n.
Description
A deficiency ratio compares an integer with the sum of its proper divisors.
A deficiency ratio compares an integer with the sum of its proper divisors.1
This tool retains negative ratios for abundant numbers instead of substituting the abundancy ratio.
When to use Deficiency Ratio Calculator
Use this tool to review negative ratios for abundant numbers instead of substituting the abundancy ratio.
How to use Deficiency Ratio Calculator and how it works
- Prepare actualN, with the units, conventions and assumptions below.
- Enter the required fields and run Deficiency Ratio Calculator.
- Read result.value using the output definitions below.
- Correct any rejected inputs and rerun; interpret the result within the stated model and its assumptions.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| actualN | Actual N. Use the units and matching context stated in the calculation below. | number | Required; integer 1–1000000; finite; other constraints below |
Require n as an integer from 1 to 1,000,000. Sum its positive proper divisors, then return (n-properDivisorSum)/n. The result is positive for deficient numbers, zero for perfect numbers and negative for abundant numbers; no absolute value is applied.
ratio=(n-aliquot(n))/n Apply the input ordering, units and branch conditions stated above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Object containing the calculated or selected fields below. | object |
| result.value | Signed deficiency ratio; negative for abundant integers. | number |
{
"input": {
"actualN": 3
},
"output": {
"result": {
"value": 0.6666666666666666
}
}
}Limitations and assumptions
The calculation uses the supplied observations and model inputs. It does not collect measurements, select a reference population or coefficient, or establish that the model applies to the actual case. The stated branch conditions and output units remain part of the result.
All fields require explicit values. Unexpected fields, wrong types, nonfinite numbers and sparse arrays are rejected. Alignment, bounds and supported-token rules are explained above; extremely large inputs or nonfinite results can also fail. Input errors differ from successful false comparisons, unavailable-domain flags and empty match lists.
Alternative or Complementary methods
Use Euler Totient Sum Approximation for a complementary operation: The totient summatory function adds the counts of positive integers coprime to each index through a finite cutoff.
Use Divisor Summatory Calculator for a complementary operation: The divisor-count summatory function totals the number of positive divisors across integers through a cutoff.
References
-
Deficiency Ratio Calculator — tool.io
Similar or alternative tools
- Euler Totient Sum Approximation
The totient summatory function adds the counts of positive integers coprime to each index through a finite cutoff.
- Divisor Summatory Calculator
The divisor-count summatory function totals the number of positive divisors across integers through a cutoff.