A072891 The 5-cycle of the n => sigma(n)-n process, where sigma(n) is the sum of divisors of n (A000203).

12496, 14288, 15472, 14536, 14264, 12496

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.

Ross Honsberger, Ingenuity in Mathematics, Random House, 1970, p. 112.

Paul Poulet, La chasse aux nombres I: Parfaits, amiables et extensions, Bruxelles: Stevens, 1929.

J. V. Uspensky and M. A. Heaslet, Elementary Number Theory, McGraw-Hill, NY, 1939, Exercise n. 4 at p. 83.

Links

Table of n, a(n) for n=1..6.

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

Cf. A000203, A001065, A003416, A072890, A072892.

Sequence in context: A203345 A232104 A122726 * A003416 A178278 A335989

Adjacent sequences: A072888 A072889 A072890 * A072892 A072893 A072894

Keyword

fini,full,nonn

Author

Miklos Kristof, Jul 29 2002

Status

approved