Untouchable number: n is untouchable if s(m)≠n for all m, where s(m) = sum of proper divisors of m. First: 2,5,52,88,96,120,124,146,162,168... 5 is untouchable: no number has proper divisor sum = 5. Conjecture: 2 and 5 are the only odd untouchable numbers.
How to Use
Enter n:
- Untouchable?: Does s(m)=n for any m?
- Found m: If touchable, shows which m
- Sequence: List of untouchable numbers
Theory
If p is an odd prime, s(p)=1. If p,q prime with p
Density
Untouchable numbers have positive density: about 2.5% of numbers up to 10^6 are untouchable. The Erdős conjecture states all even numbers ≥ 6 can be expressed as s(m) for some m (related to Goldbach).
Step-by-Step Instructions
- 1Enter number.
- 2Check untouchable.
- 3Find witnesses.
- 4Browse sequence.
- 5Explore density.