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A072890
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The 28-cycle of the n => sigma(n)-n process, where sigma(n) is the sum of divisors of n (A000203).
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6
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14316, 19116, 31704, 47616, 83328, 177792, 295488, 629072, 589786, 294896, 358336, 418904, 366556, 274924, 275444, 243760, 376736, 381028, 285778, 152990, 122410, 97946, 48976, 45946, 22976, 22744, 19916, 17716, 14316
(list;
graph;
refs;
listen;
history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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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
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REFERENCES
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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.
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LINKS
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Paul Poulet, Query 4865, L'Intermédiaire des Mathématiciens, Vol. 25 (1918), pp. 100-101.
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FORMULA
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a(28+n) = a(n).
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MATHEMATICA
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NestList[DivisorSigma[1, #]-#&, 14316, 28] (* Harvey P. Dale, Oct 27 2013 *)
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CROSSREFS
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KEYWORD
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fini,full,nonn
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AUTHOR
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STATUS
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approved
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