Amicable Pair Sum Calculator
Sum only after independently recomputedamicablepairrelationss(a)=b/s(b)=a; not existing pair boolean only. Explicit bounded resource/branch and actual observations or independently verified parameters; no unproved infinite assertion certified.
Description
An amicable pair requires each integer's proper-divisor sum to equal the other integer.
An amicable pair requires each integer's proper-divisor sum to equal the other integer.1
This tool verifies both finite relations before returning the pair's sum.
When to use Amicable Pair Sum Calculator
Use this tool to verify both finite relations before returning the pair's sum.
How to use Amicable Pair Sum Calculator and how it works
- Prepare actualFirst, actualSecond, with the units, conventions and assumptions below.
- Enter the required fields and run Amicable Pair Sum Calculator.
- Read result.verifiedAmicablePairSum 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 |
|---|---|---|---|
| actualFirst | Actual First. Use the units and matching context stated in the calculation below. | number | Required; integer 1–1000000; finite; other constraints below |
| actualSecond | Actual Second. Use the units and matching context stated in the calculation below. | number | Required; integer 1–1000000; finite; other constraints below |
Require distinct positive integers a and b, each at most 1,000,000. Compute their proper-divisor sums and reject the pair unless aliquot(a)=b and aliquot(b)=a. Return a+b only for a verified finite amicable pair; this is not an amicable-number search.
require aliquot(a)=b and aliquot(b)=a; value=a+b 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.verifiedAmicablePairSum | Sum of the two integers after checking both proper-divisor-sum identities. | number |
{
"input": {
"actualFirst": 220,
"actualSecond": 284
},
"output": {
"result": {
"verifiedAmicablePairSum": 504
}
}
}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
-
Amicable Pair Sum 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.