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 A072891). 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, pp. 28-29.
Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B7, p. 95.
C. Stanley Ogilvy, Tomorrow's math, unsolved problems for the amateur,Oxford University Press, 2nd ed., 1972, p. 113.
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(28+n) = a(n).
MATHEMATICA
NestList[DivisorSigma[1, #]-#&, 14316, 28] (* Harvey P. Dale, Oct 27 2013 *)
CROSSREFS
KEYWORD
fini,full,nonn
AUTHOR
Miklos Kristof, Jul 29 2002
STATUS
approved