Sociable numbers form aliquot cycles of length k ≥ 3. The first sociable cycle (k=5): 12496→14288→15472→14536→14264→12496. Perfect: k=1, amicable: k=2, sociable: k≥3. Only about 200 sociable chains are known.
How to Use
Enter n:
- Chain: Follow aliquot sums
- Cycle: Detect if returns to n
- Length: The cycle period k
Known Chains
First sociable chain found by Poulet (1918): 12496→14288→15472→14536→14264→12496. Most known sociable chains have length 4 or 28. No chain of length 3 has ever been found — it's conjectured none exist.
Open Problems
- Do sociable chains of length 3 exist? (Conjectured: no)
- Are there infinitely many sociable chains?
- What lengths are possible?
Step-by-Step Instructions
- 1Enter number.
- 2Iterate aliquot.
- 3Check for cycle.
- 4Find chain length.
- 5View full cycle.