Weird Number Checker
Check exact weirdness as abundance with no subset of distinct proper divisors summing to n; bounded 0/1 knapsack, not abundance alone or an exhaustive integer classification beyond caller n.
Description
A weird number is abundant but cannot be formed by summing a subset of its distinct proper divisors.
A weird number is abundant but cannot be formed by summing a subset of its distinct proper divisors. Abundance alone is therefore insufficient to classify it.1
Check exact weirdness as abundance with no subset of distinct proper divisors summing to n; bounded 0/1 knapsack, not abundance alone or an exhaustive integer classification beyond caller n.
When to use Weird Number Checker
Use this tool to check exact weirdness as abundance with no subset of distinct proper divisors summing to n; bounded 0/1 knapsack, not abundance alone or an exhaustive integer classification beyond caller n.
Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
How to use Weird Number Checker and understand its results
- Choose the integer, sequence, coefficients or function parameters for your calculation. Follow the stated ordering, domain and size limits.
- Enter candidateInteger using the field table and calculation rules, then run the tool.
- Read properDivisorSum, isAbundant, isSemiperfect, isWeird. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| candidateInteger | Candidate integer | number | Required |
Enter an integer from 1 to 20,000. Enumerate distinct proper divisors and use descending 0/1 subset-sum updates so each divisor is used at most once. Return the divisor sum and abundance, semiperfectness and weirdness flags; divisor count times n must not exceed one million.
weird = proper-divisor sum > n and no divisor subset sums to n Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| properDivisorSum | Proper divisor sum | number |
| isAbundant | Is abundant | boolean |
| isSemiperfect | Is semiperfect | boolean |
| isWeird | Is weird | boolean |
{
"input": {
"candidateInteger": 70
},
"output": {
"properDivisorSum": 74,
"isAbundant": true,
"isSemiperfect": false,
"isWeird": true
}
}Limitations and assumptions
The exact check applies only to the supplied bounded integer. It does not classify an unbounded family.
Numeric inputs and returned numeric values must be finite; an unrepresentable returned value produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors. A successfully returned false flag is an evaluated outcome; its meaning is explained above.
Alternative or Complementary methods
Use Sociable Chain Length 3 Checker: Check exact three-cycle in proper-divisor sum iteration; fixed perfect numbers and amicable two-cycles are not mislabelled length-three sociable cycles; out-of-domain intermediate refused. For a complementary task, use Vampire Number Checker: Find all unordered equal-digit factor fangs whose combined decimal multiset matches candidate; both trailing-zero fangs excluded, 1–6 digit bounded search and odd lengths false.
References
-
Weird Number Checker — tool.io
Similar or alternative tools
- Sociable Chain Length 3 Checker
Check exact three-cycle in proper-divisor sum iteration; fixed perfect numbers and amicable two-cycles are not mislabelled length-three sociable cycles; out-of-domain intermediate refused.
- Vampire Number Checker
Find all unordered equal-digit factor fangs whose combined decimal multiset matches candidate; both trailing-zero fangs excluded, 1–6 digit bounded search and odd lengths false.