Factorion Checker
Check whether a nonnegative decimal integer equals the sum of factorials of its digits, including 0!=1 and an input resource limit of 200 characters.
Description
A factorion equals the sum of the factorials of its decimal digits.
A factorion equals the sum of the factorials of its decimal digits. The zero digit contributes one because 0! is one.1
The tool returns isFactorion. The indexing and output conventions below determine how to read these values.
When to use Factorion Checker
Use this for the following task: Check whether a nonnegative decimal integer equals the sum of factorials of its digits, including 0!=1 and an input resource limit of 200 characters. Use the input and output conventions below to reproduce the intended mathematical quantity.
How to use Factorion Checker and understand its results
- Choose the required indexes, integers or sequence entries. Preserve decimal-string encodings where the field table specifies strings.
- Enter n according to the field table, then run the tool.
- Read isFactorion. A true flag means the candidate meets the stated property; false means it does not.
- If the flag is false, review the candidate and definition. A well-formed nonmember is different from a rejected input.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| n | Nonnegative decimal integer | string (integer/arbitrary); maximum text length 200; pattern ^(0|[1-9][0-9]*)$ | Required |
Precompute exact BigInt factorials for digits zero through nine, sum the entries for the input text and compare with the parsed integer.
membership ⇔ n=Σ factorial(decimal digit) The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| isFactorion | Whether n equals its digit-factorial sum | boolean |
{
"input": {
"n": "145"
},
"output": {
"isFactorion": true
}
}Limitations and assumptions
Only nonnegative decimal integers with no leading zeros and at most 200 characters are accepted. No digit permutations or complete factorion catalogue is generated.
Use the declared integer bounds and string formats. Large exact outputs remain decimal strings; numerical approximations use ordinary floating-point arithmetic. A rejected input is different from a valid zero count or false membership flag.
Alternative or Complementary methods
Choose Münchhausen Digit Self-Power Checker when you need its operation: Check whether n equals the sum of d^d over its decimal digits under an explicit 0^0 convention of zero or one, using exact integers up to 200 input characters. Choose Dudeney Number Checker for the complementary operation: Check whether a nonnegative decimal integer equals the cube of the sum of its decimal digits, using exact arithmetic and a 200-character input resource limit.
Background reference: OEIS A014080.
References
-
OEIS A014080 — OEIS Foundation
Similar or alternative tools
- Münchhausen Digit Self-Power Checker
Check whether n equals the sum of d^d over its decimal digits under an explicit 0^0 convention of zero or one, using exact integers up to 200 input characters.
- Dudeney Number Checker
Check whether a nonnegative decimal integer equals the cube of the sum of its decimal digits, using exact arithmetic and a 200-character input resource limit.