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

Author

Miklos Kristof, Jul 29 2002

Keywords

• fini
• full
• nonn

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.

Crossrefs

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

Programs

Mathematica

NestWhileList[DivisorSigma[1, #] - # &, 12496, UnsameQ, All] (* Amiram Eldar, Mar 24 2024 *)

Formula

a(5+n) = a(n).