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Week 9 · OEISOpen
Primary source

Aliquot Sequence 276 — Wandering Forever?

Intermediate· Posed 1888A008892

Problem

Aliquot sequence: start at nn, iterate s(n)=s(n) = (sum of proper divisors). Terminates at 00, enters a perfect/amicable/sociable cycle, or diverges. For n=276n = 276, does it ever terminate?

Why it matters

Catalan's 1888 conjecture, extended by Dickson in 1913, says every aliquot sequence is bounded: it reaches 1 or eventually enters a cycle. For the “Lehmer five” 276, 552, 564, 660, and 966, termination, periodicity, and unbounded growth are still unresolved. Long computations do not logically distinguish those outcomes.

Progress so far

The current aliquot.de database still classifies 276 as an open-end sequence. An ascending computed prefix cannot exclude an unfactored next step or a later prime or cycle. Guy–Selfridge “guides” motivate divergence heuristics, but they do not prove that 276 diverges.

Further reading

💡 Explore together, one line at a time(0 contributions)

Contributions are not ranked by popularity. Curator feedback names what is clear or reproducible, and peer signals mean someone understood or actually reproduced it.

What did you notice?

You do not need a complete proof. A small observation can open the next path.

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