OFFSET
1,1
COMMENTS
Called a "sociable" chain.
One of the two aliquot cycles of length greater than 2 that were discovered by Belgian mathematician Paul Poulet (1887-1946) in 1918 (the second is A072890). They were the only known such cycles until 1965 (see A072892). - Amiram Eldar, Mar 24 2024
REFERENCES
Albert H. Beiler, Recreations in the Theory of Numbers: The Queen of Mathematics Entertains, New York: Dover Publications, 1964, Chapter IV, p. 28.
Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B7, p. 95.
Paul Poulet, La chasse aux nombres I: Parfaits, amiables et extensions, Bruxelles: Stevens, 1929.
LINKS
Robert D. Carmichael, Empirical Results in the Theory of Numbers, The Mathematics Teacher, Vol. 14, No. 6 (1921), pp. 305-310; alternative link. See p. 309.
Leonard Eugene Dickson, History of the Theory of Numbers, Vol. I: Divisibility and Primality, Washington, Carnegie Institution of Washington, 1919, p. 50.
Paul Poulet, Query 4865, L'Intermédiaire des Mathématiciens, Vol. 25 (1918), pp. 100-101.
Eric Weisstein's World of Mathematics, Sociable Numbers.
Wikipedia, Sociable number.
FORMULA
a(5+n) = a(n).
MATHEMATICA
NestWhileList[DivisorSigma[1, #] - # &, 12496, UnsameQ, All] (* Amiram Eldar, Mar 24 2024 *)
CROSSREFS
KEYWORD
fini,full,nonn
AUTHOR
Miklos Kristof, Jul 29 2002
STATUS
approved