Sphenic Number Checker
Check whether n is the product of exactly three distinct primes, each with exponent one; trial division is limited to n≤10¹².
Description
A sphenic number is the product of exactly three distinct primes.
A sphenic number is the product of exactly three distinct primes. Repeated factors disqualify a number even when it has three distinct prime divisors.1
The tool returns isSphenic. The indexing and output conventions below determine how to read these values.
When to use Sphenic Number Checker
Use this for the following task: Check whether n is the product of exactly three distinct primes, each with exponent one; trial division is limited to n≤10¹². Use the input and output conventions below to reproduce the intended mathematical quantity.
How to use Sphenic Number 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 isSphenic. 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 | Positive integer (trial-division resource limit 10^12) | integer; minimum 1; maximum 1000000000000 | Required |
Factor the positive bounded integer by trial division and examine the number of distinct factors and every exponent.
sphenic ⇔ factorization has three prime factors, each exponent one The symbols and boundary conditions refer to the supplied fields and the implementation described above.
| Output field | Meaning | Value type |
|---|---|---|
| isSphenic | Whether n is sphenic | boolean |
{
"input": {
"n": 30
},
"output": {
"isSphenic": true
}
}Limitations and assumptions
Inputs are at most 10¹². The result is a membership flag, with no factorization returned; one is not sphenic.
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 Distinct Prime Factor Count when you need its operation: Return ω(n), the number of distinct prime factors, with ω(1)=0 and trial division limited to n≤10¹². Choose Prime Factor Count with Multiplicity for the complementary operation: Return Ω(n), the total number of prime factors counting their exponents, with Ω(1)=0 and trial division limited to n≤10¹².
Background reference: OEIS A007304.
References
-
OEIS A007304 — OEIS Foundation
Similar or alternative tools
- Distinct Prime Factor Count
Return ω(n), the number of distinct prime factors, with ω(1)=0 and trial division limited to n≤10¹².
- Prime Factor Count with Multiplicity
Return Ω(n), the total number of prime factors counting their exponents, with Ω(1)=0 and trial division limited to n≤10¹².