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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 (1888) and Dickson (1913) conjectured all aliquot sequences terminate. But Lehmer (1965) found that 276, 552, 564, 660, 966 — Lehmer's Five — show no sign of terminating after thousands of terms. One of the oldest open computational problems.

Progress so far

The sequence from n=276n = 276 has been computed to over 2000 terms reaching 178+ digits (BOINC / aliqueit project, ongoing). Behavior: average increase via large composite "guides" (Guy & Selfridge 1975). Richard Guy conjectured Catalan–Dickson is false — most sequences diverge.

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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