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A072890 The 28-cycle of the n => sigma(n)-n process, where sigma(n) is the sum of divisors of n (A000203).

%I A072890 #25 Feb 16 2025 08:32:46
%S A072890 14316,19116,31704,47616,83328,177792,295488,629072,589786,294896,
%T A072890 358336,418904,366556,274924,275444,243760,376736,381028,285778,
%U A072890 152990,122410,97946,48976,45946,22976,22744,19916,17716,14316
%N A072890 The 28-cycle of the n => sigma(n)-n process, where sigma(n) is the sum of divisors of n (A000203).
%C A072890 Called a "sociable" chain.
%C A072890 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
%D A072890 Albert H. Beiler, Recreations in the Theory of Numbers: The Queen of Mathematics Entertains, New York: Dover Publications, 1964, Chapter IV, pp. 28-29.
%D A072890 Richard K. Guy, Unsolved Problems in Number Theory, 3rd Edition, Springer, 2004, Section B7, p. 95.
%D A072890 C. Stanley Ogilvy, Tomorrow's math, unsolved problems for the amateur,Oxford University Press, 2nd ed., 1972, p. 113.
%D A072890 Paul Poulet, La chasse aux nombres I: Parfaits, amiables et extensions, Bruxelles: Stevens, 1929.
%H A072890 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 A072890 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 A072890 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 A072890 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SociableNumbers.html">Sociable Numbers</a>.
%H A072890 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sociable_number">Sociable number</a>.
%F A072890 a(28+n) = a(n).
%t A072890 NestList[DivisorSigma[1,#]-#&,14316,28] (* _Harvey P. Dale_, Oct 27 2013 *)
%Y A072890 Cf. A000203, A001065, A072891, A072892.
%K A072890 fini,full,nonn
%O A072890 1,1
%A A072890 _Miklos Kristof_, Jul 29 2002