A072891 - OEIS

%I #14 Mar 24 2024 04:00:11

%S 12496,14288,15472,14536,14264,12496

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

%C Called a "sociable" chain.

%C 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

%D Albert H. Beiler, Recreations in the Theory of Numbers: The Queen of Mathematics Entertains, New York: Dover Publications, 1964, Chapter IV, p. 28.

%D Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B7, p. 95.

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

%H Robert D. Carmichael, <a href="https://doi.org/10.5951/MT.14.6.0305">Empirical Results in the Theory of Numbers</a>, The Mathematics Teacher, Vol. 14, No. 6 (1921), pp. 305-310; <a href="https://www.jstor.org/stable/27950349">alternative link</a>. See p. 309.

%H Leonard Eugene Dickson, <a href="https://archive.org/details/historyoftheoryo01dick_1/page/50/mode/2up">History of the Theory of Numbers, Vol. I: Divisibility and Primality</a>,  Washington, Carnegie Institution of Washington, 1919, p. 50.

%H Paul Poulet, <a href="https://proofwiki.org/wiki/Book:Article/Paul_Poulet/4865">Query 4865</a>, L'Intermédiaire des Mathématiciens, Vol. 25 (1918), pp. 100-101.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SociableNumbers.html">Sociable Numbers</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sociable_number">Sociable number</a>.

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

%t NestWhileList[DivisorSigma[1, #] - # &, 12496, UnsameQ, All] (* _Amiram Eldar_, Mar 24 2024 *)

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

%K fini,full,nonn

%O 1,1

%A _Miklos Kristof_, Jul 29 2002