A072890 - OEIS

A072890

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

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

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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 A072891). 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, 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.

LINKS

Table of n, a(n) for n=1..29.

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(28+n) = a(n).

MATHEMATICA

NestList[DivisorSigma[1, #]-#&, 14316, 28] (* Harvey P. Dale, Oct 27 2013 *)

CROSSREFS

Cf. A000203, A001065, A072891, A072892.

Sequence in context: A115554 A106726 A064965 * A249314 A249207 A049442

Adjacent sequences: A072887 A072888 A072889 * A072891 A072892 A072893